
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 an ellipse $C: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$ with its left vertex and right focus being $A$ and $F$ respectively, and its right directrix being $m$.

(1) If there is no point $Q$ on line $m$ such that $\Delta AFQ$ is an isosceles triangle, find the range of the eccentricity of the ellipse.

(2) Under the conditions of (1), when $e$ takes the maximum value, the coordinates of point $A$ are $(-2, 0)$. Let $B$, $M$, and $N$ be three points on the ellipse, and $\overrightarrow{OB} = \frac{3}{5}\overrightarrow{OM} + \frac{4}{5}\overrightarrow{ON}$. Find the equation of the circle with the midpoint of segment $MN$ as its center and passing through points $A$ and $F$.

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