
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
Given a triangle $ABC$ with $A(1, -2, -1)$, $B(0, -3, 1)$, and $C(2, -2, 1)$. If the vector $\vec{n}$ is perpendicular to plane $ABC$ and $|\vec{n}| = \sqrt{21}$, find the coordinates of $\vec{n}$.

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