
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
The inscribed circle of triangle $ABC$ is tangent to $\overline{AB}$ at $P$, and its radius is $30$. Given that $AP=26$ and $PB=32$, find the perimeter of the triangle $ABC$, assuming the altitude from $C$ to $\overline{AB}$ is $96$.

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