
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 $C$ centered at the origin with one focus at $F\_1(-3,0)$ and an asymptote with equation $\sqrt {5}x-2y=0$.

(I) Find the equation of hyperbola $C$.
(II) If a line $l$ with slope $k (k \neq 0)$ intersects hyperbola $C$ at two distinct points $M$ and $N$, and the area of the triangle formed by the perpendicular bisector of segment $MN$ and both coordinate axes is $\frac{81}{2}$, find the range of $k$.

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