
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
Calculate the volume of the tetrahedron with vertices at points \( A_{1} \), \( A_{2} \), \( A_{3} \), \( A_{4} \) and its height dropped from vertex \( A_{4} \) to the face \( A_{1} A_{2} A_{3} \).

Given coordinates:
\[ A_{1}(-1, -5, 2) \]
\[ A_{2}(-6, 0, -3) \]
\[ A_{3}(3, 6, -3) \]
\[ A_{4}(-10, 6, 7) \]

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