
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 regular dodecahedron has side length $s$. A plane cuts the dodecahedron but is not parallel to any of its faces, intersecting through the midpoints of a set of edges that form a pentagon. Find the area of the polygon formed by the intersection. Express your answer in terms of $s$.
A) $\frac{5s^2(\sqrt{5} + 1)}{8}$
B) $\frac{5s^2(\sqrt{5} + 1)}{16}$
C) $\frac{5s^2(\sqrt{5} - 1)}{16}$
D) $\frac{5s^2}{16}$
E) $\frac{5s^2(\sqrt{5} + 1)}{32}$

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