
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 triangle $ABC$, three factories are located at the vertices $A$, $B$, and $C$. Given that $AB = AC = 5$ and $BC = 6$, a sewage treatment plant is to be built at point $P$ on the sides of $\triangle ABC$, and three sewage pipelines $AP$, $BP$, and $CP$ are to be constructed. Find the minimum value of $AP + BP + CP$.

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