
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  $ABC$ ,  $A'$ ,  $B'$ , and  $C'$  are on the sides  $BC$ ,  $AC$ , and  $AB$ , respectively. Given that  $AA'$ ,  $BB'$ , and  $CC'$  are concurrent at the point  $O$ , and that \[\frac{AO}{OA'}+\frac{BO}{OB'}+\frac{CO}{OC'}=92,\] find \[\frac{AO}{OA'}\cdot \frac{BO}{OB'}\cdot \frac{CO}{OC'}.\]

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