
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
The foot of the perpendicular from the origin to a plane is at the point $(10, -5, 2)$. Find the equation of the plane in the form \[ Ax + By + Cz + D = 0, \] where \(A\), \(B\), \(C\), and \(D\) are integers such that \(A > 0\) and \(\gcd(|A|, |B|, |C|, |D|) = 1\).

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