
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 a triangle $\triangle PQR$ with an area of $15$, points $L, M, N$ are located on sides $PQ, QR,$ and $RP$ respectively. Suppose $PL = 3$, $LQ = 2$, and triangles $\triangle PLM$ and quadrilateral $LMNQ$ have equal areas. Determine the area of triangle $\triangle PLM$.
A) $6$
B) $7.2$
C) $9$
D) $10.8$
E) $12$

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