
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 $EFGH$, point $J$ is on $\overline{EF}$ so that $\frac{EJ}{EF} = \frac{1}{4}$ and point $K$ is on $\overline{EH}$ so that $\frac{EK}{EH} = \frac{1}{5}$. Line segment $\overline{JK}$ intersects the diagonal $\overline{FG}$ at point $L$. Find $\frac{FG}{FL}$.

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