
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
In triangle $XYZ$, points $X'$, $Y'$, and $Z'$ are on sides $YZ$, $XZ$, and $XY$ respectively. Given that $XX'$, $YY'$, and $ZZ'$ are concurrent at point $P$, and that $\frac{XP}{PX'} + \frac{YP}{PY'} + \frac{ZP}{PZ'} = 100$, find $\frac{XP}{PX'} \cdot \frac{YP}{PY'} \cdot \frac{ZP}{PZ'}$.

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