
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 triangle $ABC$ be such that $AB = AC$ and $O$ is the centroid of $ABC$. Given that $OQ = 5$ cm, where $Q$ is the midpoint of side $BC$, determine the length of $OP$ in centimeters, where $P$ is the midpoint of side $AB$.
A) 7.5 cm
B) 10 cm
C) 15 cm
D) 12.5 cm
E) 5 cm

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