You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]


Q:

what would be the right permission to allow everything else but overwriting or creating a database?

I have a test environment where the AD group mycompany\developers is currently sysadmin.
Recently I have had some issues, specially regarding to people restoring databases. My concerns are:

sometimes the database is involved in replication 
the permissions are overwritten - the correct way is to save the
current permissions before the restore and re-apply them after the restore.
Have you checked the current available disk space in all drivers,
specially those used in this restore?
there might be other people using or working on that specific
    database, and restoring over it without communication can cause
    someone's else work being lost
in the dev environment the databases can be in simple recovery mode.
Have you shrunk the log and changed the database to simple recovery
mode.
in this particular case, the full backup for every user database is
going to run automatically every night. but anyways, have you
checked for scheduled backups?
have you deleted from the server the backup that you used to do the
restore?
the folders and drives or data and logs are different in live and
test. are you sure you moved the files to the right places?
Have you had a look at orphaned users and logins?

I particularly have concerns when developers create new databases, even in the dev environment. why?
because they start by creating the database in dev and then just ask me to copy it to live. 
have you done any capacity planning for this database? how big it should be and how much it would grow in a month?

have you isolated or considered different filegroups for demainding
objects\indexes?
Have you checked the current available disk space in all drivers,
    specially those used in this DB creation?
how big is the transaction log and why? Initially I like to set it
1.5 times the biggest clustered index.
what are the autogrowth settings?
what are the current permissions?

I have realised some people are not so easy to deal with, I rather reduce their power over that server.
I don't want to do their jobs, but I would like to restrict them from creating new databases, or overwriting existing ones, either by restoring or by attaching files, etc.
They still should be able to create and run jobs, create\alter any object withing user databases, create logins, grant permissions etc...
Basically the question is:
How to limit the power of a current sysadmin?
I thought about not granting sysadmin but a set of server permissions (excluding those to create/alter databases) that would allow them to do everything else.
what would that set of server permissions be?

A:

TL;DR
In order to restrict the DEVs from doing anything "wrong" you have to at least remove the sysadmin SQL Server role.
Let's start
You could assign your DEVs the db_owner database role for each individual database. However that role will permit a user to perform a BACKUP DATABASE ... or BACKUP LOG ... which you mentioned you don't want them to be able to perform.
Solutions
Beginning with SQL Server 2014 you can then restrict a SQL Server Login with the db_owner role further removing individual privileges/permissions. One example is to remove the backup privilege on the database and transaction log level by issuing the following commands on the database:
USE <database_name>
GO
DENY BACKUP DATABASE TO <database_principal>
GO
DENY BACKUP LOG TO <database_principal>

Reference: DENY Database Permissions (Transact-SQL) (Microsoft Docs)
There are three levels of permissions.
GRANT  : You are granted/granting a specific permission  
REVOKE : A previously granted/denied permission is revoked (removed) again  
DENY   : You are denied/denying a specific permission  

Alternative
Now because DENY has precedence over GRANT you could use the alternative solution of creating a new database role and adding the <database_principals> to that role:
USE <database_name>
GO
CREATE ROLE [deny_backup]
GO
DENY BACKUP DATABASE TO [deny_backup]
GO
DENY BACKUP LOG TO [deny_backup]
GO
EXEC sp_addrolemember N'deny_backup', N'<database_principal>'
GO

Reference: Restrict Backup permission to user (Social MSDN)
Step by Step Guide
Because some people are sceptical about statements I have made in this post, I am adding the individual steps to show you how you can indeed DENY permissions from a SQL Login even though that login has the db_owner role.

Creating and Mapping SQL Login
Let's create a SQL Login and assign it the db_owner database role:

Deny Backup Database permissions
Now we switch to a higher privileged account like sa or a Windows Login (which would be you, the DBA asking this question) that has the sysadmin SQL Server role and DENY the right to backup database from the database principal hot2use:

In a perfect world you would also need to submit a DENY BACKUP LOG TO hot2use too.
Log in to server with hot2use and back up database
Seeing as hot2use has the db_owner database role for the Test database, we log in with hot2use...

...and try to back up the database:

Well that doesn't work and is what we expected. This is because the SQL Server login hot2use no longer has the privilege to back up the database even though the login still has the database role db_owner:
SQL Login wants to hack permissions
Seeing as the SQL Server login has the db_owner role and according to some people he can assign himself the permissions back, let's try that out:

(The test was conducted in a fresh database SQL Server Query window)
Summary
If you DENY permissions with a higher privileged account, then these privileges can not be GRANTed back from the lesser privileged account, even thought the SQL Login (e.g. hot2use) should have these privileges from the database role db_owner. This is something that changed in SQL Server 2014 (yes, the tests were conducted on a SQL Server 2014 instance).

Additional ressources
You can further restrict permissions according to the official overview which can be found here:
Permissions (Database Engine)
Further recommended reading: 
Getting Started with Database Engine Permissions
Wait, restores...
Oh yes, we only denied the BACKUP DATABASE privilege didn't we? That has nothing to do with RESTORE DATABASE, or does it? Let's find out. I'll create a database backup with a higher privileged account/login:

Seems to work. Let's switch back to the hot2use SQL Server Query window and restore the backup:

As you can see, it isn't going to work, because the BACKUP DATABASE privilege also restricts the restore capability of that SQL Server login.
No backup privilege = No restore privilege.
How about DENY BACKUP DATABASE FROM SYSADMIN?
Well, since you asked. Let's try it out. I'll leave out the screen shots that show how I revoked the database role. 
I assigned the SQL Login the sysadmin SQL Server role with:
ALTER SERVER ROLE [sysadmin] ADD MEMBER [hot2use]
GO

...and then removed the permission to backup the database with the above mentioned DENY BACKUP DATABASE.. commands and then performed a database backup with:
backup database Test to disk = 'C:\temp\Test_Full_Backup_20171121.bak'

... which resulted in: 

So you can't DENY permissions from a SQL Login with the sysadmin Server role, but you can DENY permissions if the SQL Login does not have the 'sysadmin' database role.
Minimal permissions required to backup / restore a database
If I assign the SQL Server login absolutely no SQL Server roles and assign only the db_backupoperator database role on a given database, then I can backup and restore the database. This is something that others believe the SQL login is unable to perform. The higher privileged account created the backup, so the lower privileged account (non-sysadmin) shouldn't be able to do a backup/restore.
After resetting all permissions of the SQL Server login hot2use to public on the server and db_backupoperator on the database level, I am presented with the following enumerated permissions:

According to others I shouldn't be able to perform a backup because I am missing a SQL Server role. 

So I can in fact backup a database if I have the db_backupoperator role. 
And again, if I DENY BACKUP DATABASE to the SQL Server login (on a SQL Server 2014 instance or greater), then I am no longer capable of backing up my database, even though I still have the db_backupoperator role on the database level:

If the SQL Login hot2use tries to REVOKE the previously denied permission then that will fail, with a similar message that I previously showed above.
Summary
Determing which permissions/privileges/roles you want to assign to your DEVs is going to be a tiring fight/issue, because they won't want to give up the  sysadmin SQL Server role. You will have to find out which SQL Server Roles and which Database Roles they will exactly require to do their job. The worst-case is that everything will stay the same. The best case is that you will be able to restrict the DEVs in their permissions/privileges.
You will at least have to remove the sysadmin SQL Server role from your DEVs in order to further restrict them from being able to do everything they want. But once that SQL Server role has been removed, you can assign them for example the db_owner role and DENY BACKUP DATABASE ... to disallow them from backing up the database or restoring it. 
The developers can still do anything they want inside the database (includig a DROP DATABASE), but they cannot perform a backup or a restore. See the following enumerated permissions for the SQL Server login hot2use with the database role db_owner but having both DENY BACKUP DATABASE ... and DENY BACKUP LOG ...:

SQL Server Login with db_owner role but without backup permissions

A:

To be able answer your question we need to know what exactly permissions at server level your developers need.
You are approaching from the wrong side: you gave them sysadmin server level role and try to limit sysadmin, but it's not possible (there were some changes in last versions, but they concern with DATA access, not administrative privileges, you can now hide your data from sysadmin, but not to limit its power in administrative tasks).
So instead of trying to DENY something to sysadmin (that is impossible) you should think what permissions should you GRANT. 
Your developers should not be members of sysadmin, otherwise it's not possible to DENY something to them.
Make a list of what your developers should be able to do, and update your question. Maybe it can be achieved by creating custom server role and by granting to it only necessary permissions, or maybe it can be done using stored procedures signed with certificate.
The most difficult thing to accomplish without sysadmin rights is this one:

They still should be able to create and run jobs

As soon as you remove your logins from sysadmin role, SQL Server Agent will disappear for them from SSMS.
To be able to use SQL Server Agent server principal should be at least a member of SQLAgentUserRole, to be able to run jobs -- a member of SQLAgentOperatorRole, you can read more on it here: SQL Server Agent Fixed Database Roles. But even SQLAgentOperatorRole is still limited compared to sysadmin, so read the article and decide if those permissions are sufficient for your devs, if no, SQL Server Agent use will require a sysadmin membership.
ABOUT RESTORE PERMISSIONS

If the database being restored does not exist, the user must have
  CREATE DATABASE permissions to be able to execute RESTORE. If the
  database exists, RESTORE permissions default to members of the
  sysadmin and dbcreator fixed server roles and the owner (dbo) of the
  database (for the FROM DATABASE_SNAPSHOT option, the database always
  exists).
RESTORE permissions are given to roles in which membership information
  is always readily available to the server. Because fixed database role
  membership can be checked only when the database is accessible and
  undamaged, which is not always the case when RESTORE is executed,
  members of the db_owner fixed database role do not have RESTORE
  permissions.

This is a cite from official MS documentation that you can read here: RESTORE Statements (Transact-SQL) under PERMISSIONS.
It clearly states that someone CANNOT restore/create database without SERVER LEVEL PERMISSIONS.
This means that to resolve your problem you don't need to deny anything at database level, it won't help you in restriction of RESTORE ability.
Who has no server permissions (membership in dbcreator or sysadmin server roles), already cannot restore/create database.
Who has these permissions, cannot lose them if you deny any database level permission.

Now, the other answerer has made a claim that I feel needs to be addressed:
“No backup privilege = No restore privilege”
Let's investigate it. Here is a simple repro.
As stated in BOL article, to be able to RESTORE a database one should be a member of dbcreator or sysadmin server roles.
So if one that is just db_owner (and certainly HAS backup permission) CANNOT restore database.
Let's create a new database, backup it, create a login that will be mapped to that database and added to db_owner database role, we'll using pictures that convince more then code..
use master;
GO

create database test;
GO

create login hot2use with password = '*****';
GO

use test;
create user hot2use from login hot2use;
exec sp_addrolemember 'db_owner', 'hot2use';
go

execute as login = 'hot2use';
select is_member('db_owner') as is_db_owner;
select HAS_PERMS_BY_NAME('test', 'database', 'backup database') as has_backup_database;
select HAS_PERMS_BY_NAME('test', 'database', 'backup log') as has_backup_log;

All 3 last queries return 1 as hot2use is db_owner, has backup database and backup log permissions.
Now we check if hot2use is sysadmin or dbcreator server role member (that are able to restore):
select IS_SRVROLEMEMBER('sysadmin') as is_sysadmin;
select IS_SRVROLEMEMBER('dbcreator') as is_dbcreator;

This code returns 0 in both cases:

Now close all the connections to test database and backup it:
backup database test to disk = 'Z:\TEMP\test_full.bak';
go

Now our hot2use tries to restore test database:
restore database test from disk = 'Z:\TEMP\test_full.bak' with replace;

Wow. 

Msg 3110, Level 14, State 1, Line 1 User does not have permission to
  RESTORE database 'test'.

How can it be that our hot2use has both backup database and backup log permissions and is not able to restore?
It's simple. Backup permission is needed to backup, to be able to restore, re-read BOL article and see WHO has RESTORE permission that is necessary to be able to RESTORE:

So to be able to RESTORE one should be a member of sysadmin or dbcreator server level roles.
Let's fix it and put our login hot2use in dbcreator role:
exec sp_addsrvrolemember 'hot2use', 'dbcreator';

Now our hot2use is able to restore:

Finally, we now DENY backup database and backup log permission to hot2use and he will retry to restore:
use test;
deny backup database to hot2use;
deny backup log to hot2use;
GO

execute as login = 'hot2use';

select is_member('db_owner') as is_db_owner;
select HAS_PERMS_BY_NAME('test', 'database', 'backup database') as has_backup_database;
select HAS_PERMS_BY_NAME('test', 'database', 'backup log') as has_backup_log;
select IS_SRVROLEMEMBER('sysadmin') as is_sysadmin;
select IS_SRVROLEMEMBER('dbcreator') as is_dbcreator;
revert;

So now hot2use has NO backup database, backup log permission, but he is still member of dbcreator server role.
Will he be able to restore?

Yes of course.
This is because, as stated in the BOL and demonstrated above, no backup permission is needed to be able to RESTORE.