
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 parallelogram $ABCD$, line $DP$ is drawn to trisect $BC$ at $N$ nearest to $B$ and meets $AB$ extended twice the length from $B$ to $A$ at $P$. From vertex $C$, line $CQ$ is drawn to trisect $AD$ at $M$ nearest to $A$ and meets the line through $B$ extended twice the length from $A$ to $B$ at $Q$. Lines $DP$ and $CQ$ meet at $O$. Determine the area of triangle $QPO$.

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