
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
Given that $AM$ and $CN$ are medians of triangle $ABC$ that intersect at point $O$, and point $P$ lies on side $AC$ such that $AP:PC = 2:1$, and $MP$ intersects $CN$ at $Q$, find the area of triangle $ABC$ in terms of the area of triangle $OMQ$.

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