
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 $ABCD$, where $\angle BAD$ is $60^{\circ}$, $AB = 2$, $AD = 5$, the bisector of $\angle BAD$ intersects the bisector of $\angle ABC$ at point $K$ and the bisector of $\angle CDA$ at point $L$. The bisector of $\angle BCD$ intersects the bisector of $\angle CDA$ at point $M$ and the bisector of $\angle ABC$ at point $N$. Find the ratio of the area of quadrilateral $KLMN$ to the area of parallelogram $ABCD$.

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