
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 \( F \) are collinear points in that order such that \( AB = BC = 1, CD = 3, \) and \( DF = 8 \). If \( P \) can be any point in space, what is the smallest possible value of \( AP^2 + BP^2 + CP^2 + DP^2 + FP^2 \)?

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