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

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