
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
Harry, Sandy, and Luna wish to meet at a point in Hogwarts that is at the centroid of their coordinates. Harry is standing at $(10, -3)$, Sandy is standing at $(2, 5)$, and Luna is standing at $(-2, 9)$. At what coordinate will they meet?

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