
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
Given a circle of radius $7$ with points $E$ and $F$ on the circle where $EF=8$ and point $G$ on the circle such that the central angle subtended by $EG$ is $\frac{\pi}{3}$. Find the length of the line segment $EG$.

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