
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

Find the distance from vertex \( A_4 \) to the face \( A_1 A_2 A_3 \).

\( A_1(2, 1, 4) \)

\( A_2(-1, 5, -2) \)

\( A_3(-7, -3, 2) \)

\( A_4(-6, -3, 6) \)

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