
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(-1, 2, 1), B(1, 2, 1), C(-1, 6, 4):
1. Calculate the area S of the parallelogram formed by vectors $\overrightarrow{AB}$ and $\overrightarrow{AC}$ as two adjacent sides.
2. If vector $\overrightarrow{a}$ is perpendicular to both vectors $\overrightarrow{AB}$ and $\overrightarrow{AC}$, and $|\overrightarrow{a}| = 10$, find the coordinates of vector $\overrightarrow{a}$.

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