
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 three points in space: A(0, 2, 3), B(-2, 1, 6), C(1, -1, 5). If the vector $\overrightarrow{n}$ is perpendicular to both vectors $\overrightarrow{AB}$ and $\overrightarrow{AC}$, and the magnitude of $\overrightarrow{n}$ is $\sqrt{3}$, then find the coordinates of vector $\overrightarrow{n}$.

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