
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 volume of a tetrahedron whose vertices are located at points with coordinates \(\left(F_{n}, F_{n+1}, F_{n+2}\right), \quad\left(F_{n+3}, F_{n+4}, F_{n+5}\right), \quad\left(F_{n+6}, F_{n+7}, F_{n+8}\right),\) and \(\left(F_{n+9}, F_{n+10}, F_{n+11}\right)\), where \(F_{i}\) is the \(i\)-th term of the Fibonacci sequence: \(1, 1, 2, 3, 5, 8 \ldots\).

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