
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
Circle $P$ on the coordinate plane has a center at $(5, -2)$. One endpoint of a diameter is located at $(1, 5)$. Determine the coordinates of the opposite endpoint of the diameter. Express your answer as an ordered pair.

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