
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
The side length of the square is divided into two segments by a diagonal, one of which is x. The value of x is the difference between the length of the side of the square, s, and the length of the other segment, \( \frac{s}{2} \). Given that the regular pentagon is inscribed in the square, what is the value of \( x \) if \( s = 12 \)?

Present the answer in LaTex format: \boxed{Your answer}
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