
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
If points A(0, 2, 3), B(-2, 1, 6), and C(1, -1, 5) are given, and $|\overrightarrow{a}| = \sqrt{3}$, and $\overrightarrow{a}$ is perpendicular to both $\overrightarrow{AB}$ and $\overrightarrow{AC}$, find the vector $\overrightarrow{a}$.

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