
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
A square with side length $s$ is divided into a pentagon and three congruent trapezoids by connecting the center of the square to points on each of its four sides. Find $x$, the length of the longer parallel side of each trapezoid, given that the pentagon and the three trapezoids all have equal area.
A) $\frac{s}{3}$  
B) $\frac{s}{2}$  
C) $\frac{2s}{3}$  
D) $s$

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