
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 the diagram below, points \( A \), \( B \), \( C \), and \( P \) are positioned such that \( PA = 3 \), \( PB = 4 \), \( PC = 5 \), and \( BC = 6 \). Additionally, angle \( \angle ABC \) is a right angle. Determine the maximum possible area of \( \triangle ABC \).

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