
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 the face \(A_{1} A_{2} A_{3}\).

\(A_{1}(0 ;-3 ; 1)\)

\(A_{2}(-4 ; 1 ; 2)\)

\(A_{3}(2 ;-1 ; 5)\)

\(A_{4}(3 ; 1 ;-4)\)

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