
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
In triangle \(ABC\), points \(D\), \(E\), and \(F\) are on sides \(\overline{BC}\), \(\overline{AC}\), and \(\overline{AB}\), respectively, such that \(BD:DC = 2:3\), \(CE:EA = 3:2\), and \(AF:FB = 2:3\). Line segments \(\overline{AD}\), \(\overline{BE}\), and \(\overline{CF}\) intersect at points \(P\), \(Q\), and \(R\), respectively. Compute \(\frac{[PQR]}{[ABC]}\).

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