
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 prism \( P-ABC \),
\[
\begin{array}{l}
\angle APB = \angle BPC = \angle CPA = 90^{\circ}, \\
PA = 4, \, PB = PC = 3.
\end{array}
\]

Find the minimum sum of the squares of the distances from any point on the base \( ABC \) to the three lateral faces.

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