
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 $A,B,C,D,E$ and $F$ lie, in that order, on $\overline{AF}$, dividing it into five segments. $AB = 1$, $BC = 2$, $CD = 1$, $DE = 1$, and $EF = 2$. Point $G$ is off the line $AF$. Point $H$ lies on $\overline{GD}$, point $J$ on $\overline{GF}$, and point $K$ lies on $\overline{GB}$. The line segments $\overline{HC}, \overline{JE}, \overline{KB}$, and $\overline{AG}$ are parallel. Find the ratio $HC/JE$.
A) $\frac{7}{8}$
B) $\frac{4}{7}$
C) $\frac{9}{8}$
D) $\frac{2}{9}$
E) $\frac{1}{2}$

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