
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 $ABC$, $AB = 10, BC = 11$, and $AC = 12$. The points $P$, $Q$, and $R$ are the midpoints of sides $\overline{AB}, \overline{BC}$, and $\overline{CA}$ respectively. Find the length of segment $OQ$ if $O$ is the centroid of triangle $ABC$ and $Q$ is the midpoint of side $BC$.
A) $\frac{1}{3} OP$
B) $\frac{2}{3} OP$
C) $\frac{1}{2} OP$
D) $\frac{1}{4} OP$

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