
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
Three factories are located at points A, B, and C. It is measured that AB=BC=5km and AC=6km. To facilitate wastewater treatment, it is desired to build a sewage treatment plant at point P somewhere on the sides of triangle ABC and to lay sewage pipes AP, BP, and CP. The minimum value of AP+BP+CP is ___ km.

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