
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
A plane passes through the point (10, -2, 5) and the normal vector to the plane is perpendicular to the vector from the origin to this point. Find the equation of the plane in the form \[Ax + By + Cz + D = 0,\] where $A$, $B$, $C$, $D$ 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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