
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 $PQR$, $PQ = 10$, $QR = 12$, and $PR = 14$. If $F$ and $G$ are points on $\overline{PQ}$ and $\overline{PR}$ such that $PF = 3$ and $PG = 5$, then find the area of triangle $PFG$.

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