
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
Suppose $ABC$ is a right triangle with the right angle at $B$ and $P$ is a point on hypotenuse $\overline{AC}$ such that $\angle{ABP} = 60^\circ$. Given that $AP = 2$ and $CP = 3$, compute the area of triangle $ABC$.

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