
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 $ABC,$ $D,$ $E,$ and $F$ are points on sides $\overline{BC},$ $\overline{CA},$ and $\overline{AB},$ respectively, such that $BD:DC = 2:3,$ $CE:EA = 1:4,$ and $AF:FB = 3:2.$ 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}
user