
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 $ABC$, the medians $AM$ and $CN$ to sides $BC$ and $AB$, respectively, intersect at point $O$. $P$ is the midpoint of side $AB$, and line $MP$ (where $M$ is still the midpoint of side $BC$) intersects line $CN$ at $Q$. Given that the area of triangle $OMQ$ is $k$, find the area of triangle $ABC$.
A) $6k$
B) $9k$
C) $12k$
D) $18k$
E) $24k$

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