
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
Write the equation of a plane passing through the point \(A\) perpendicular to the vector \(\overrightarrow{BC}\).

Given:
\[ A(5, -1, 2) \]
\[ B(2, -4, 3) \]
\[ C(4, -1, 3) \]

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