
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 $A_{4}$ onto face $A_{1} A_{2} A_{3}$.

$A_{1}(1, 3, 0)$

$A_{2}(4, -1, 2)$

$A_{3}(3, 0, 1)$

$A_{4}(-4, 3, 5)$

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