
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 hyperbola C with its center at the origin, the right focus is at (2, 0), and the left vertex is at $(\sqrt{3}, 0)$.
(1) Find the equation of hyperbola C.
(2) If a line $y=kx+m$ ($k \neq 0, m \neq 0$) intersects the hyperbola C at two distinct points M and N, and the perpendicular bisector of the line segment MN passes through the point A (0, -1), find the range of values for the real number m.

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