
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
Let $P_1P_2P_3P_4P_5$ be a regular pentagon whose apothem is $3$. Point $Q_i$ on each side $P_iP_{i+1}$ (where $P_6 = P_1$) is such that $P_iQ_i$ is a third of $P_iP_{i+1}$. Determine the area of the pentagon formed by points $Q_1, Q_2, Q_3, Q_4, Q_5$.
A) 12.5
B) 13.5
C) 14.5
D) 15.5

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