
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
Points $A, B, C, D, E, F, G,$ and $H$ lie, in that order, on $\overline{AH}$, dividing it into seven segments with lengths 1, 2, 1, 1, 2, 1 respectively. Point $I$ is not on line $\overline{AH}$. Points $J$ and $K$ are on lines $\overline{IF}$ and $\overline{IH}$ respectively. The line segments $\overline{JC}, \overline{KE},$ and $\overline{AI}$ are parallel. Calculate the ratio $JC/KE$.

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