
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 seven points \( P_{1}, P_{2}, P_{3}, P_{4}, P_{5}, P_{6}, P_{7} \) are arranged in order along a straight line (not necessarily equidistant), find the position of point P such that the sum of the lengths \( PP_{1}, PP_{2}, \ldots, PP_{7} \) is minimized.

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