
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 point $M(2,2)$, a line $L$ passes through it and intersects the hyperbola $x^{2}- \frac{y^{2}}{4}=1$ at points $A$ and $B$. Point $M$ is the midpoint of segment $AB$.
(1) Find the equation of line $L$;
(2) Find the length of segment $AB$.

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