
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 $ABC$, points $D$, $E$, and $F$ are on the sides $BC$, $AC$, and $AB$, respectively. Given that $AD$, $BE$, and $CF$ are concurrent at the point $P$, and that $\frac{AP}{PD}+\frac{BP}{PE}+\frac{CP}{PF}=100$, find $\frac{AP}{PD}\cdot \frac{BP}{PE}\cdot \frac{CP}{PF}$.

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