
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 triangular pyramid \(P-ABC\), \(\angle APC = \angle CPB = \angle BPA = \frac{\pi}{2}\), and \(PA = PB = 3\), \(PC = 4\). Also, \(M\) is a point within the base \(ABC\). What is the minimum value of the sum of the squares of the distances from \(M\) to the three lateral faces of the triangular pyramid?

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