
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 $A, B, C, D, E, F,$ and $G$ lie, in that order, on line $\overline{AG}$, with $\overline{AB} = \overline{CD} = \overline{EF} = 1$ and $\overline{BC} = \overline{DE} = 2$. Point $H$ is off $\overline{AG}$, and points $I$ and $J$ lie on $\overline{HD}$ and $\overline{HG}$, respectively. The line segments $\overline{IC}, \overline{JE},$ and $\overline{AH}$ are parallel. Moreover, $\overline{DJ}$ is parallel to $\overline{AH}$. Find the ratio $\frac{IC}{JE}$.
A) $\frac{4}{3}$
B) $\frac{5}{3}$
C) $\frac{3}{2}$
D) $\frac{5}{4}$
E) $2$

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