
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 order, on line segment $\overline{AF}$. The lengths of the segments $\overline{AB}, \overline{BC}, \overline{CD}, \overline{DE},$ and $\overline{EF}$ are 1, 2, 3, 4, and 5 respectively. Point $G$ is not on line $\overline{AF}$. Points $H$ lies on $\overline{GC}$ and point $J$ lies on $\overline{GB}$. The line segments $\overline{HD}, \overline{JE},$ and $\overline{AG}$ are parallel. Find the ratio $HD/JE$.

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