
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 the points $A_{1}, A_{2}, A_{3}, A_{4}$ and its height dropped from the vertex $A_{4}$ onto the face $A_{1} A_{2} A_{3}$.

$A_{1}(1, 2, 0)$

$A_{2}(3, 0, -3)$

$A_{3}(5, 2, 6)$

$A_{4}(8, 4, -9)$

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