
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
Let points on a parabola be \(A = (2,0), B = (5,3),\) and \(C = (p, -p^2 + 8p - 12)\) where \(2 \le p \le 5.\) Calculate the maximum possible area of triangle ABC.

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