
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
If \( P_1P_2P_3P_4P_5P_6 \) is a regular hexagon with an apothem of \( 3 \), and \( Q_i \) is the midpoint of side \( P_iP_{i+1} \) for \( i=1,2,3 \), calculate the area of triangle \( Q_1Q_2Q_3 \).
A) \( \frac{3\sqrt{3}}{4} \)
B) \( \frac{9\sqrt{3}}{4} \)
C) \( 6\sqrt{3} \)
D) \( \frac{9}{2} \)

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