
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 bisecting $BC$ at $N$ and meeting $AB$ (extended) at $P$, and line $CQ$ is drawn bisecting side $AD$ at $M$ and meeting $AB$ (extended) at $Q$. Given that the area of parallelogram $ABCD$ is $k$, calculate the area of the triangle $QPO$.

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