
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 $XYZ$, $X'$, $Y'$, and $Z'$ are on the sides $YZ$, $XZ$, and $XY$, respectively. Suppose $XX'$, $YY'$, and $ZZ'$ are concurrent at the point $O$ and that $\frac{XO}{OX'}+\frac{YO}{OY'}+\frac{ZO}{OZ'} = 105$. Find $\frac{XO}{OX'} \cdot \frac{YO}{OY'} \cdot \frac{ZO}{OZ'}$.

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