
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 the area of the parallelogram $ABCD$ is $240$, $E$ and $H$ are the midpoints of sides $AD$ and $AB$ respectively. Point $G$ is on side $BC$ such that $BG = 2GC$, and point $F$ is on side $CD$ such that $DF = 3FC$. Point $K$ is on side $AC$ such that the area of $\triangle EKF$ is 33. Find the area of $\triangle HKG$.

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