
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
Regular hexagon $PQRSTU$ is composed of six smaller non-equilateral trapezoids, such as $PQVW$, shown in boldface in the diagram. By connecting alternate vertices, we obtain a larger square $PRCT$, also shown in boldface. Calculate the ratio $[\trapezoid PQVW]/[\square PRCT]$. Assume all sides of the original hexagon and the inner square are equal length $s$.

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