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]


! H0 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
! H0 X
! H0 X   libAtoms+QUIP: atomistic simulation library
! H0 X
! H0 X   Portions of this code were written by
! H0 X     Albert Bartok-Partay, Silvia Cereda, Gabor Csanyi, James Kermode,
! H0 X     Ivan Solt, Wojciech Szlachta, Csilla Varnai, Steven Winfield.
! H0 X
! H0 X   Copyright 2006-2010.
! H0 X
! H0 X   These portions of the source code are released under the GNU General
! H0 X   Public License, version 2, http://www.gnu.org/copyleft/gpl.html
! H0 X
! H0 X   If you would like to license the source code under different terms,
! H0 X   please contact Gabor Csanyi, <PRESIDIO_ANONYMIZED_EMAIL_ADDRESS>
! H0 X
! H0 X   Portions of this code were written by Noam Bernstein as part of
! H0 X   his employment for the U.S. Government, and are not subject
! H0 X   to copyright in the USA.
! H0 X
! H0 X
! H0 X   When using this software, please cite the following reference:
! H0 X
! H0 X   http://www.libatoms.org
! H0 X
! H0 X  Additional contributions by
! H0 X    Alessio Comisso, Chiara Gattinoni, and Gianpietro Moras
! H0 X
! H0 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

#include "error.inc"
module frametools_module
use system_module
use linearalgebra_module
use atoms_types_module
use atoms_module
use quaternions_module
implicit none
private


public :: atoms_mark

public :: mark_cylinder, mark_sphere

private :: ft_rotate
public :: rotate
interface rotate
   module procedure ft_rotate
end interface rotate

contains

!% Mark atoms according to the results of a callback function `mark_f`
!%
!% The integer property `mark_name` will be set to `mark_value` for
!% the atoms for which the function `mark_f(at, i, periodic, f_i_data,
!% f_r_data[, error])` returns true, where `i` is the atom index and
!% the other arguments are passed along from those given to `atoms_mark`.
subroutine atoms_mark(this, mark_f, f_i_data, f_r_data, periodic, mark_name, mark_value, intersection, error)
  type(atoms), intent(inout) :: this
  interface
    function mark_f(at, i, periodic, i_data, r_data, error)
    use system_module
    use atoms_module
      type(atoms), intent(inout) :: at
      integer, intent(in) :: i
      logical, intent(in) :: periodic
      integer, intent(in), optional :: i_data(:)
      real(dp), intent(in), optional :: r_data(:)
      integer, intent(out), optional :: error
      logical mark_f
    end function mark_f
  end interface
  integer, intent(in), optional :: f_i_data(:) !% Integer data passed along to `mark_f` function
  real(dp), intent(in), optional :: f_r_data(:) !% Real data passed along to `mark_f` function
  logical, intent(in), optional :: periodic !% Passed along to `mark_f` function
  character(len=*), intent(in), optional :: mark_name !% Name of integer property to set the marks in
  integer, intent(in), optional :: mark_value !% Value with which to mark atoms
  logical, intent(in), optional :: intersection !% If true, only consider atoms where mark property is already non-zero
  integer, intent(out), optional :: error

  integer :: i
  character(len=128) :: my_mark_name
  integer :: my_mark_value
  logical :: my_intersection, my_periodic
  integer, pointer :: mark(:)

  INIT_ERROR(error)

  my_mark_name = optional_default("mark", mark_name)
  my_mark_value = optional_default(1, mark_value)
  my_intersection = optional_default(.false., intersection)
  my_periodic = optional_default(.true., periodic)

  if (.not. assign_pointer(this, trim(my_mark_name), mark)) then
      call add_property(this, trim(my_mark_name), 0, ptr=mark)
  else
      call assign_property_pointer(this, trim(my_mark_name), mark, error=error)
  endif

  do i=1, this%N
    if (my_intersection .and. mark(i) == 0) cycle ! if we're doing intersection and this one isn't already marked, skip it
    if (my_intersection) mark(i) = 0 ! if we're doing intersection, set mark to .false., and it'll will be set to true if it's marked in the current shape
    if (mark_f(this, i, my_periodic, f_i_data, f_r_data, error=error)) then
      mark(i) = my_mark_value
    endif
    PASS_ERROR(error)
  end do
end subroutine atoms_mark

function is_in_cylinder_f(this, i, periodic, i_data, r_data, error)
  type(atoms), intent(inout) :: this
  integer, intent(in) :: i
  logical, intent(in) :: periodic
  integer, intent(in), optional :: i_data(:)
  real(dp), intent(in), optional :: r_data(:)
  integer, intent(out), optional :: error
  logical is_in_cylinder_f

  logical :: my_periodic
  real(dp) :: delta_p(3), v(3), r

  INIT_ERROR(error)

  if (present(i_data)) then
     RAISE_ERROR("is_in_cylinder_f doesn't take i_data", error)
  endif
  if (.not.present(r_data)) then
     RAISE_ERROR("is_in_cylinder_f requires r_data", error)
  endif
  if (size(r_data) /= 7) then
     RAISE_ERROR("is_in_cylinder_f requires [px py pz vx vy vz r] in cylinder", error)
  endif

  if (periodic) then
     delta_p = diff_min_image(this, i, r_data(1:3))
  else
     delta_p = this%pos(:,i) - r_data(1:3)
  endif
  v = r_data(4:6)
  v = v/norm(v)
  r = r_data(7)

  delta_p = delta_p - v*(v .dot. delta_p)
  if (r > 0.0_dp) then
     is_in_cylinder_f = (norm(delta_p) < r)
  else
     is_in_cylinder_f = (norm(delta_p) >= -r)
  endif
end function is_in_cylinder_f

function is_in_sphere_f(this, i, periodic, i_data, r_data, error)
  type(atoms), intent(inout) :: this
  integer, intent(in) :: i
  logical, intent(in) :: periodic
  integer, intent(in), optional :: i_data(:)
  real(dp), intent(in), optional :: r_data(:)
  integer, intent(out), optional :: error
  logical is_in_sphere_f

  real(dp) :: dr, r

  INIT_ERROR(error)

  if (present(i_data)) then
     RAISE_ERROR("is_in_sphere_f doesn't take i_data", error)
  endif
  if (.not.present(r_data)) then
     RAISE_ERROR("is_in_sphere_f requires r_data", error)
  endif
  if (size(r_data) /= 4) then
     RAISE_ERROR("is_in_sphere_f requires [px py pz r] in sphere", error)
  endif

  if (periodic) then
     dr = distance_min_image(this, i, r_data(1:3))
  else
     dr = norm(this%pos(:,i)-r_data(1:3))
  endif
  r = r_data(4)

  if (r > 0.0_dp) then
     is_in_sphere_f = (dr < r)
  else
     is_in_sphere_f = (dr >= -r)
  endif
end function is_in_sphere_f


!% Mark atoms in a cylinder centred on the point `p` with axis `v` and radius `r`
subroutine mark_cylinder(this, p, v, r, periodic, mark_name, mark_value, intersection)
  type(atoms), intent(inout) :: this
  real(dp), intent(in) :: p(3), v(3), r
  character(len=*), intent(in), optional :: mark_name
  integer, intent(in), optional :: mark_value
  logical, intent(in), optional :: periodic, intersection

  call atoms_mark(this, is_in_cylinder_f, f_r_data=(/ p, v, r /), periodic=periodic, mark_name=mark_name, mark_value=mark_value, intersection=intersection)
end subroutine mark_cylinder

!% Mark atoms in a cylinder centred on the point `p` with radius `r`
subroutine mark_sphere(this, p, r, periodic, mark_name, mark_value, intersection)
  type(atoms), intent(inout) :: this
  real(dp), intent(in) :: p(3), r
  character(len=*), intent(in), optional :: mark_name
  integer, intent(in), optional :: mark_value
  logical, intent(in), optional :: periodic, intersection

  call atoms_mark(this, is_in_sphere_f, f_r_data=(/ p, r /), periodic=periodic, mark_name=mark_name, mark_value=mark_value, intersection=intersection)
end subroutine mark_sphere

!% Rotate `field`, which should be a vector field with shape `(3, N)`,
!% e.g. atomic positions array around `axis` by `angle`, centering the
!% rotation on `origin`
subroutine ft_rotate(field, axis, angle, origin)
  real(dp), intent(inout) :: field(:,:)
  real(dp), intent(in) :: axis(3)
  real(dp), intent(in) :: angle
  real(dp), intent(in), optional :: origin(3)

  real(dp) :: dr(3)
  type(Quaternion) :: Q
  integer i, N

  Q = rotation(axis, angle)
  
  N = size(field,2)

  do i=1, N
    if (present(origin)) then
      field(:,i) = field(:,i)-origin
    endif
    call rotate(field(:,i), Q)
  end do
end subroutine ft_rotate


end module frametools_module