
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 $D$ are in space such that each of $\overline{TA}$, $\overline{TB}$, $\overline{TC}$, and $\overline{TD}$ is perpendicular to the other three. If $TA = TB = 15$, $TC = 9$, and $TD = 3$, and $D$ is located on the line segment $AB$ extending beyond $B$, then what is the distance from $T$ to face $ABC$?

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