
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 $D, E, F$ are on sides $\overline{BC}, \overline{CA}, \overline{AB}$ respectively, such that $BD:DC = CE:EA = AF:FB = 3:2$. The lines $\overline{AD}, \overline{BE}, \overline{CF}$ intersect at points $P, Q, R$ respectively. Determine $\frac{[PQR]}{[ABC]}$.

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