
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 lie 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 $7$ times the length of $\overline{FH}$. What fraction of the length of $\overline{GH}$ is the length of $\overline{EF}$?
A) $\frac{1}{6}$
B) $\frac{1}{7}$
C) $\frac{1}{8}$
D) $\frac{1}{9}$
E) $\frac{1}{10}$

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