
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 $P_1, P_2, ..., P_8$ placed on a straight line in a given sequence, denote a point $Q$ on this line for which the sum $s = PQ_1 + PQ_2 + ... + PQ_8$ of undirected distances is minimal. Find the location of the point $Q$ that results in the smallest value of $s$.

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