
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
Point $P_1, P_2,\cdots,P_9$ are given on a straight line, in the order stated. Let $P$ be an arbitrarily selected point on the line and let $s$ be the sum of the undirected lengths $PP_1, PP_2, \cdots , PP_9$. Determine the location of $P$ that minimizes the sum $s$.

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