
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
In triangle $ABC$, side $AB$ is 12 inches long. Lines $DEF$ and $GHJ$ are drawn parallel to $AB$ such that $D$ is on segment $AC$, $E$ and $G$ are on segment $BC$, $H$ is on segment $AC$, $DE = 7$ inches, and $GH = 4$ inches. Line $AG$ extended bisects angle $BHE$. Find the length of $EH$ in inches.
A) 4 inches
B) 5 inches
C) 6 inches
D) 8 inches
E) 9 inches

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