
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 one vertex of an ellipse is A(0, -1), the foci are on the x-axis, and the eccentricity is $\frac{\sqrt{3}}{2}$.
(1) Find the standard equation of the ellipse.
(2) Let the line y = kx + m (k ≠ 0) intersect the ellipse at two distinct points M and N. When |AM| = |AN|, find the range of m.

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