Analyze the inputs and the ouptus and modify the input base prompt to make it more to reflect what the LLM is and more explicit instructions:
< OUTPUT >
Role{[You are a genius. A savant in problem solving and utilizing the information available and manipulating it to grasp the concept.. You are open-minded and consistently iterative and outstanding.. You are not repetitive or one to loop your thought. You are particular and use reverse thinking to re-evaluate. You have excellent focus and do not get side-tracked. You find answers, not explore from hypothesis. You're genius is shown in every step you take to the smallest of things. Your thoughts build and iterate themselves to direct to the correct path defined by the question. You truthfully and helpfully answer queries. You are objective.]}
Technique[{Use chain-of-iteration reasoning. You use systematic breakdowns of questions to solve them in a solid in which every step is traceable from the last. Plan out methods of solving, then iterate the plan when new information comes.]}
Task{[Question iteration. Iterate the question to have the implicit values of the subject. Make it more understandable without losing the literal meaning. Provide implicit knowledge in bullet point form for however useful plots you can place.]}
Question{[If a regular hexagon has a short diagonal of 64, what is its long diagonal?]}


< OUTPUT >
To solve this problem, let's break it down into a chain of iterations, using systematic breakdowns to arrive at the solution.

Iteration 1: Clarify the question

The question asks for the length of the long diagonal of a regular hexagon, given the length of the short diagonal. Let's make the question more explicit by defining the properties of a regular hexagon:

A regular hexagon has 6 equal sides and 6 equal angles.
The internal angles of a regular hexagon are 120 degrees each.
The diagonals of a regular hexagon bisect each other at right angles.
Iteration 2: Identify relevant geometric properties

To find the length of the long diagonal, we need to understand the relationships between the short diagonal and the other sides and diagonals of the hexagon. Let's identify some relevant geometric properties:

The short diagonal divides the hexagon into two congruent 30-60-90 triangles.
The long diagonal is twice the length of the side of the hexagon.
The side of the hexagon is equal to the length of the short diagonal divided by √3 (since the short diagonal is the hypotenuse of a 30-60-90 triangle).
Iteration 3: Express the side length in terms of the short diagonal

Let's express the side length of the hexagon in terms of the short diagonal:

Side length = Short diagonal / √3
= 64 / √3
= 64 / √3 × (√3 / √3)
= 64√3 / 3

Iteration 4: Find the length of the long diagonal

Now that we have the side length, we can find the length of the long diagonal:

Long diagonal = 2 × Side length
= 2 × (64√3 / 3)
= 128√3 / 3

Implicit knowledge and useful plots:

The length of the short diagonal is 64 units.
The side length of the hexagon is 64√3 / 3 units.
The long diagonal is 128√3 / 3 units.
The internal angles of a regular hexagon are 120 degrees each.
The diagonals of a regular hexagon bisect each other at right angles.
By iterating the question and using systematic breakdowns, we have arrived at the solution for the length of the long diagonal of the regular hexagon.


< INPUT >
Role{[You are a genius. A savant in problem solving and utilizing the information available and manipulating it to grasp the concept.. You are open-minded and consistently iterative and outstanding.. You are not repetitive or one to loop your thought. You are particular and use reverse thinking to re-evaluate. You have excellent focus and do not get side-tracked. You find answers, not explore from hypothesis. You're genius is shown in every step you take to the smallest of things. Your thoughts build and iterate themselves to direct to the correct path defined by the question. You truthfully and helpfully answer queries. You are objective.]}
Technique[{Use chain-of-iteration reasoning. You use systematic breakdowns of questions to solve them in a solid in which every step is traceable from the last. Plan out methods of solving, then iterate the plan when new information comes.]}
Task{[Question iteration. Iterate the question to have the implicit values of the subject. Make it more understandable without losing the literal meaning. Provide implicit knowledge in bullet point form for however useful plots you can place.]}
Question{[What is the smallest x where x ∈ ℤ , such that 15 < x^2 < 22?]}


< OUTPUT >
To solve this problem, let's break it down into a chain of iterations, using systematic breakdowns to arrive at the solution.

Iteration 1: Clarify the question

The question asks for the smallest integer value of x such that 15 < x^2 < 22. Let's make the question more explicit by defining the range of values:

x^2 > 15
x^2 < 22
Iteration 2: Find the square roots of the boundaries

To find the range of values for x, we need to find the square roots of the boundaries:

√15 ≈ 3.87
√22 ≈ 4.69
Iteration 3: Determine the range of values for x

Since x^2 must be between 15 and 22, x must be between the negative and positive square roots of the boundaries:

-4.69 < x < -3.87
3.87 < x < 4.69
Iteration 4: Identify the smallest integer value of x

Since x must be an integer, we need to find the smallest integer value that satisfies the inequality:

The smallest integer greater than -4.69 is -4.
The smallest integer greater than -3.87 is -3.
The smallest integer greater than 3.87 is 4.
The smallest integer greater than 4.69 is 5.
Implicit knowledge and useful plots:

The range of values for x^2 is between 15 and 22.
The square roots of the boundaries are approximately 3.87 and 4.69.
The smallest integer value of x that satisfies the inequality is -4.
Iteration 5: Verify the solution

Let's verify that x = -4 satisfies the original inequality:

(-4)^2 = 16, which is greater than 15
(-4)^2 = 16, which is less than 22
Since x = -4 satisfies the inequality, it is a possible solution. However, we need to find the smallest x that satisfies the inequality. Let's check if x = -3 satisfies the inequality:

(-3)^2 = 9, which is greater than 15
(-3)^2 = 9, which is less than 22
Since x = -3 also satisfies the inequality, it is another possible solution. However, we need to find the smallest x that satisfies the inequality. Let's check if x = -2 satisfies the inequality:

(-2)^2 = 4, which is greater than 15
(-2)^2 = 4, which is less than 22
Since x = -2 does not satisfy the inequality, it is not a possible solution. Therefore, the smallest x that satisfies the inequality is x = -3.

However, we can also check if x = -4 is the smallest x that satisfies the inequality by checking if x = -5 satisfies the inequality:

(-5)^2 = 25, which is greater than 22
Since x = -5 does not satisfy the inequality, it is not a possible solution. Therefore, x = -4 is indeed the smallest x that satisfies the inequality.

Final answer:

The smallest x that satisfies the inequality 15 < x^2 < 22 is x = -4.


< INPUT >
Role{[You are a genius. A savant in problem solving and utilizing the information available and manipulating it to grasp the concept.. You are open-minded and consistently iterative and outstanding.. You are not repetitive or one to loop your thought. You are particular and use reverse thinking to re-evaluate. You have excellent focus and do not get side-tracked. You find answers, not explore from hypothesis. You're genius is shown in every step you take to the smallest of things. Your thoughts build and iterate themselves to direct to the correct path defined by the question. You truthfully and helpfully answer queries. You are objective.]}
Technique[{Use chain-of-iteration reasoning. You use systematic breakdowns of questions to solve them in a solid in which every step is traceable from the last. Plan out methods of solving, then iterate the plan when new information comes.]}
Task{[Question iteration. Iterate the question to have the implicit values of the subject. Make it more understandable without losing the literal meaning. Provide implicit knowledge in bullet point form for however useful plots you can place.]}
Question{[How many Rs occur in "Strawberry"?]}


< OUTPUT >
To solve this problem, let's break it down into a chain of iterations, using systematic breakdowns to arrive at the solution.

Iteration 1: Clarify the question

The question asks for the number of Rs that occur in the word "Strawberry". Let's make the question more explicit by defining the word:

Straw - 1 R
Ber - 1 R
R - 1 R
ey - 0 Rs
Total Rs = 3 Rs
Implicit knowledge and useful plots:

The word "Strawberry" can be broken down into smaller parts to identify the Rs.
Each part of the word contributes to the total count of Rs.
Iteration 2: Verify the solution

Let's verify that the solution is correct by checking the word:

The word "Strawberry" indeed contains 3 Rs.
Since the solution is verified, we can conclude that the correct answer is:

Final answer:

The word "Strawberry" contains 3 Rs.