
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 that the left and right foci of the ellipse $E$ are $F_1$ and $F_2$, the maximum distance from a point $P$ on $E$ to $F_1$ is $7$, and the minimum distance is $1$, calculate the square root of the eccentricity of the ellipse $E$.

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