
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
\( A, B, C, D, \) and \( E \) are collinear in that order with \( AB = 3, BC = 1, CD = 5, \) and \( DE = 4 \). Determine the smallest possible value of \( AP^2 + BP^2 + CP^2 + DP^2 + EP^2 \) if \( P \) is any point on the line containing all these points.

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