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

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