
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
Let  $M$  be the midpoint of side  $AC$  of the triangle  $ABC$ . Let  $P$  be a point on the side  $BC$ . If  $O$  is the point of intersection of  $AP$  and  $BM$  and  $BO = BP$ , determine the ratio  $\frac{OM}{PC}$  .

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