
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 $A'$, $B'$, and $C'$ lie on sides $BC$, $AC$, and $AB$, respectively. Lines $AA'$, $BB'$, and $CC'$ intersect at point $O$. Given that $\frac{AO}{OA'}+\frac{BO}{OB'}+\frac{CO}{OC'}=56$, find the value of $\left(\frac{AO}{OA'} \cdot \frac{BO}{OB'} \cdot \frac{CO}{OC'}\right)^2$.

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