
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
Find the equation of the plane passing through the points $(-1, 2, 3)$, $(2, -1, 4)$, and $(0, 0, 5)$ that is perpendicular to the plane given by $x + 2y + 3z = 6$. Write your answer in the form $Ax + By + Cz + D = 0$, where $A, B, C, D$ are integers, $A > 0$, and $\gcd(|A|, |B|, |C|, |D|) = 1$.

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