
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 diagram shows a regular dodecagon and a square, whose vertices are also vertices of the dodecagon. What is the value of the ratio of the area of the square to the area of the dodecagon?

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