
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 the plane passing through the point \( A \) and perpendicular to the vector \( \overrightarrow{BC} \).

\( A(-7, 1, -4) \)

\( B(8, 11, -3) \)

\( C(9, 9, -1) \)

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