
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 octagon P_1P_2P_3P_4P_5P_6P_7P_8 has an apothem (distance from the center to the midpoint of a side) of 3. If Q_i is the midpoint of the side P_iP_{i+1} for i=1,3,5,7, determine the area of quadrilateral Q_1Q_3Q_5Q_7.

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