
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 with lengths 2, 2, 3, 3, and 4 respectively. Point $G$ is not on line $AF$. Point $H$ lies on $\overline{GD}$, and point $J$ lies on $\overline{GF}$. The line segments $\overline{HC}, \overline{JE},$ and $\overline{AG}$ are parallel. Find the ratio $HC/JE$.
- A) $\frac{5}{4}$
- B) $\frac{4}{3}$
- C) $\frac{3}{2}$
- D) $\frac{5}{3}$
- E) $2$

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