
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 \(E\) and \(F\) are positioned on line segment \(\overline{GH}\). The length of \(\overline{GE}\) is \(3\) times the length of \(\overline{EH}\), and the length of \(\overline{GF}\) is \(8\) times the length of \(\overline{FH}\). Determine the fraction of the length of \(\overline{EF}\) in terms of the length of \(\overline{GH}\).
A) \(\frac{1}{9}\)
B) \(\frac{1}{12}\)
C) \(\frac{1}{18}\)
D) \(\frac{5}{36}\)
E) \(\frac{1}{8}\)

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