
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 $X$, $Y$, $Z$, and $P$ are in space such that each of $\overline{PX}$, $\overline{PY}$, and $\overline{PZ}$ is perpendicular to the other two. If $PX = PY = 10$, and $PZ = 8$, what is the distance from $P$ to face $XYZ$?

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