
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
Given triangle $\triangle ABC$, all distinct points, $P, Q$, and $R$ are located on the sides $AB, BC$, and $CA$, respectively, with $AP = 3, PB = 2$. If $\triangle ABQ$ and quadrilateral $PBRQ$ have equal areas and the area of triangle $\triangle ABC$ is $15$, calculate the area of $\triangle ABQ$.

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