
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
Points \(A\), \(B\), \(C\), and \(T\) are in space such that each of \(\overline{TA}\), \(\overline{TB}\), and \(\overline{TC}\) is perpendicular to the other two. If \(TA = TB = 12\) and \(TC = 10\), then what is the volume of pyramid \(TABC\)?

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