
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 $O$ be the centroid of triangle $ABC$, intersecting medians $AM$ and $CQ$ at the same point. Triangle $ABC$ is isosceles with $AB = AC$. If $OQ$ is 5 inches, then determine $OC$.
A) 2.5 inches
B) 5 inches
C) 10 inches
D) 15 inches
E) 7.5 inches

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