
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 $DEF$, $D'$, $E'$, and $F'$ are on the sides $EF$, $FD$, and $DE$, respectively. Suppose $DD'$, $EE'$, and $FF'$ are concurrent at point $P$, and that $\frac{DP}{PD'}+\frac{EP}{PE'}+\frac{FP}{PF'}=100$. Find $\frac{DP}{PD'}\cdot \frac{EP}{PE'}\cdot \frac{FP}{PF'}$.

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