
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
Given points \( P_1, P_2, \ldots, P_9 \) on a straight line, in the order stated (not necessarily evenly spaced). 
Let \( P \) be an arbitrarily selected point on the line, and let \( s \) be the sum of the undirected lengths
\( PP_1, PP_2, \ldots, PP_9 \). Determine \( P \) so that \( s \) is minimized.
A) \( P_1 \)
B) \( P_2 \)
C) \( P_3 \)
D) \( P_5 \) (Correct answer)
E) \( P_9 \)

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