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:

Calendar Recurring/Repeating Events - Best Storage Method

I am building a custom events system, and if you have a repeating event that looks like this:
Event A repeats every 4 days starting on March 3, 2011
or 
Event B repeats every 2 weeks on Tuesday starting on March 1, 2011
How can I store that in a Database in a way that would make it simple to lookup. I don't want performance issues if there are a large number of events, and I have to go through each and every one when rendering the calendar.

A:

Storing "Simple" Repeating Patterns
For my PHP/MySQL based calendar, I wanted to store repeating/recurring event information as efficiently as possibly. I didn't want to have a large number of rows, and I wanted to easily lookup all events that would take place on a specific date.
The method below is great at storing repeating information that occurs at regular intervals, such as every day, every n days, every week, every month every year, etc etc. This includes every Tuesday and Thursday type patterns as well, because they are stored separately as every week starting on a Tuesday and every week starting on a Thursday.
Assuming I have two tables, one called events like this:
ID    NAME
1     Sample Event
2     Another Event

And a table called events_meta like this:
ID    event_id      meta_key           meta_value
1     1             repeat_start       1299132000
2     1             repeat_interval_1  432000

With repeat_start being a date with no time as a unix timestamp, and repeat_interval an amount in seconds between intervals (432000 is 5 days). 
repeat_interval_1 goes with repeat_start of the ID 1. So if I have an event that repeats every Tuesday and every Thursday, the repeat_interval would be 604800 (7 days), and there would be 2 repeat_starts and 2 repeat_intervals. The table would look like this:
ID    event_id      meta_key           meta_value
1     1             repeat_start       1298959200 -- This is for the Tuesday repeat
2     1             repeat_interval_1  604800
3     1             repeat_start       1299132000 -- This is for the Thursday repeat
4     1             repeat_interval_3  604800
5     2             repeat_start       1299132000
6     2             repeat_interval_5  1          -- Using 1 as a value gives us an event that only happens once

Then, if you have a calendar that loops through every day, grabbing the events for the day it's at, the query would look like this:
SELECT EV.*
FROM `events` EV
RIGHT JOIN `events_meta` EM1 ON EM1.`event_id` = EV.`id`
RIGHT JOIN `events_meta` EM2 ON EM2.`meta_key` = CONCAT( 'repeat_interval_', EM1.`id` )
WHERE EM1.meta_key = 'repeat_start'
    AND (
        ( CASE ( 1299132000 - EM1.`meta_value` )
            WHEN 0
              THEN 1
            ELSE ( 1299132000 - EM1.`meta_value` )
          END
        ) / EM2.`meta_value`
    ) = 1
LIMIT 0 , 30

Replacing {current_timestamp} with the unix timestamp for the current date (Minus the time, so the hour, minute and second values would be set to 0).
Hopefully this will help somebody else too!

Storing "Complex" Repeating Patterns
This method is better suited for storing complex patterns such as 
Event A repeats every month on the 3rd of the month starting on March 3, 2011 
or 
Event A repeats Friday of the 2nd week of the month starting on March 11, 2011
I'd recommend combining this with the above system for the most flexibility. The tables for this should like like:
ID    NAME
1     Sample Event
2     Another Event

And a table called events_meta like this:
ID    event_id      meta_key           meta_value
1     1             repeat_start       1299132000 -- March 3rd, 2011
2     1             repeat_year_1      *
3     1             repeat_month_1     *
4     1             repeat_week_im_1   2
5     1             repeat_weekday_1   6

repeat_week_im represents the week of the current month, which could be between 1 and 5 potentially. repeat_weekday in the day of the week, 1-7.
Now assuming you are looping through the days/weeks to create a month view in your calendar, you could compose a query like this:
SELECT EV . *
FROM `events` AS EV
JOIN `events_meta` EM1 ON EM1.event_id = EV.id
AND EM1.meta_key = 'repeat_start'
LEFT JOIN `events_meta` EM2 ON EM2.meta_key = CONCAT( 'repeat_year_', EM1.id )
LEFT JOIN `events_meta` EM3 ON EM3.meta_key = CONCAT( 'repeat_month_', EM1.id )
LEFT JOIN `events_meta` EM4 ON EM4.meta_key = CONCAT( 'repeat_week_im_', EM1.id )
LEFT JOIN `events_meta` EM5 ON EM5.meta_key = CONCAT( 'repeat_weekday_', EM1.id )
WHERE (
  EM2.meta_value =2011
  OR EM2.meta_value = '*'
)
AND (
  EM3.meta_value =4
  OR EM3.meta_value = '*'
)
AND (
  EM4.meta_value =2
  OR EM4.meta_value = '*'
)
AND (
  EM5.meta_value =6
  OR EM5.meta_value = '*'
)
AND EM1.meta_value >= {current_timestamp}
LIMIT 0 , 30

This combined with the above method could be combined to cover most repeating/recurring event patterns. If I've missed anything please leave a comment.

A:

While the currently accepted answer was a huge help to me, I wanted to share some useful modifications that simplify the queries and also increase performance.

"Simple" Repeat Events
To handle events which recur at regular intervals, such as:
Repeat every other day 

or 
Repeat every week on Tuesday 

You should create two tables, one called events like this:
ID    NAME
1     Sample Event
2     Another Event

And a table called events_meta like this:
ID    event_id      repeat_start       repeat_interval
1     1             1369008000         604800            -- Repeats every Monday after May 20th 2013
1     1             1369008000         604800            -- Also repeats every Friday after May 20th 2013

With repeat_start being a unix timestamp date with no time (1369008000 corresponds to May 20th 2013) , and repeat_interval an amount in seconds between intervals (604800 is 7 days).   
By looping over each day in the calendar you can get repeat events using this simple query:
SELECT EV.*
FROM `events` EV
RIGHT JOIN `events_meta` EM1 ON EM1.`event_id` = EV.`id`
WHERE  (( 1299736800 - repeat_start) % repeat_interval = 0 )

Just substitute in the unix-timestamp (1299736800) for each date in your calendar.
Note the use of the modulo (% sign). This symbol is like regular division, but returns the ''remainder'' instead of the quotient, and as such is 0 whenever the current date is an exact multiple of the repeat_interval from the repeat_start.
Performance Comparison
This is significantly faster than the previously suggested "meta_keys"-based answer, which was as follows:
SELECT EV.*
FROM `events` EV
RIGHT JOIN `events_meta` EM1 ON EM1.`event_id` = EV.`id`
RIGHT JOIN `events_meta` EM2 ON EM2.`meta_key` = CONCAT( 'repeat_interval_', EM1.`id` )
WHERE EM1.meta_key = 'repeat_start'
    AND (
        ( CASE ( 1299132000 - EM1.`meta_value` )
            WHEN 0
              THEN 1
            ELSE ( 1299132000 - EM1.`meta_value` )
          END
        ) / EM2.`meta_value`
    ) = 1

If you run EXPLAIN this query, you'll note that it required the use of a join buffer:
+----+-------------+-------+--------+---------------+---------+---------+------------------+------+--------------------------------+
| id | select_type | table | type   | possible_keys | key     | key_len | ref              | rows | Extra                          |
+----+-------------+-------+--------+---------------+---------+---------+------------------+------+--------------------------------+
|  1 | SIMPLE      | EM1   | ALL    | NULL          | NULL    | NULL    | NULL             |    2 | Using where                    |
|  1 | SIMPLE      | EV    | eq_ref | PRIMARY       | PRIMARY | 4       | bcs.EM1.event_id |    1 |                                |
|  1 | SIMPLE      | EM2   | ALL    | NULL          | NULL    | NULL    | NULL             |    2 | Using where; Using join buffer |
+----+-------------+-------+--------+---------------+---------+---------+------------------+------+--------------------------------+

The solution with 1 join above requires no such buffer.

"Complex" Patterns
You can add support for more complex types to support these types of repeat rules:
Event A repeats every month on the 3rd of the month starting on March 3, 2011

or
Event A repeats second Friday of the month starting on March 11, 2011

Your events table can look exactly the same:
ID    NAME
1     Sample Event
2     Another Event

Then to add support for these complex rules add columns to events_meta like so:
ID    event_id      repeat_start       repeat_interval    repeat_year    repeat_month    repeat_day    repeat_week    repeat_weekday
1     1             1369008000         604800             NULL           NULL            NULL          NULL           NULL             -- Repeats every Monday after May 20, 2013
1     1             1368144000         604800             NULL           NULL            NULL          NULL           NULL             -- Repeats every Friday after May 10, 2013
2     2             1369008000         NULL               2013           *               *             2              5                -- Repeats on Friday of the 2nd week in every month    

Note that you simply need to either specify a repeat_interval or a set of repeat_year, repeat_month, repeat_day, repeat_week, and repeat_weekday data.
This makes selection of both types simultaneously very simple. Just loop through each day and fill in the correct values, (1370563200 for June 7th 2013, and then the year, month, day, week number and weekday as follows):
SELECT EV.*
FROM `events` EV
RIGHT JOIN `events_meta` EM1 ON EM1.`event_id` = EV.`id`
WHERE  (( 1370563200 - repeat_start) % repeat_interval = 0 )
  OR ( 
    (repeat_year = 2013 OR repeat_year = '*' )
    AND
    (repeat_month = 6 OR repeat_month = '*' )
    AND
    (repeat_day = 7 OR repeat_day = '*' )
    AND
    (repeat_week = 2 OR repeat_week = '*' )
    AND
    (repeat_weekday = 5 OR repeat_weekday = '*' )
    AND repeat_start <= 1370563200
  )

This returns all events that repeat on the Friday of the 2nd week, as well as any events that repeat every Friday, so it returns both event ID 1 and 2:
ID    NAME
1     Sample Event
2     Another Event

*Sidenote in the above SQL I used PHP Date's default weekday indexes, so "5" for Friday 

Hope this helps others as much as the original answer helped me!

A:

Enhancement: replace timestamp with date
As a small enhancement to the accepted answer that was subsequently refined by ahoffner - it is possible to use a date format rather than timestamp.  The advantages are:

readable dates in the database
no issue with the years > 2038 and timestamp
removes need to be careful with timestamps that are based on seasonally adjusted dates i.e. in the UK 28th June starts one hour earlier than 28th December so deriving a timestamp from a date can break the recursion algorithm.

to do this, change the DB repeat_start to be stored as type 'date' and repeat_interval now hold days rather than seconds.  i.e. 7 for a repeat of 7 days.
change the sql line:
WHERE (( 1370563200 - repeat_start) % repeat_interval = 0 )

to:
WHERE ( DATEDIFF( '2013-6-7', repeat_start ) % repeat_interval = 0)

everything else remains the same. Simples!