
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 $\overline{BC}$, $\overline{CA}$, and $\overline{AB}$ respectively, where $BD:DC = 2:3$, $CE:EA = 2:3$, and $AF:FB = 2:3$. Line segments $\overline{AD}$, $\overline{BE}$, and $\overline{CF}$ intersect. Let $P$ be the intersection of $\overline{AD}$ and $\overline{CF}$, $Q$ be the intersection of $\overline{AD}$ and $\overline{BE}$, and $R$ be the intersection of $\overline{BE}$ and $\overline{CF}$. Compute $\frac{[PQR]}{[ABC]}$.

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