
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
Two hexagons, $ABCDEF$ and $GHIJEF$, share a common side $EF$ and have identical areas of 36 each. If $K$ is the point on side $AB$ such that $AK:KB = 1:2$, and $K$ is also the midpoint of $GH$, find the total area of the polygon $AGKIJEFB$.

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