
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 line $\overline{AH}$, dividing it into seven equal segments, each of length 2. Point $I$ is not on line $\overline{AH}$. Point $J$ lies on $\overline{ID}$, and point $K$ lies on $\overline{IH}$. The line segments $\overline{JC}, \overline{KE},$ and $\overline{AI}$ are parallel. Find the ratio $\frac{JC}{KE}$.
A) $\frac{3}{4}$  
B) $\frac{5}{4}$  
C) $\frac{6}{4}$  
D) $\frac{7}{4}$

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