
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
A circle $O$ is defined by the equation $x^{2}+y^{2}=4$ and contains a point $P(-1,1)$.
(1) When a chord $AB$ is bisected by point $P$, find the equation of the line $AB$.
(2) Lines $l_{1}$ and $l_{2}$ are two tangent lines of circle $O$ such that $l_{1} \perp l_{2}$, and their feet are at point $Q$. Find the trajectory equation of the midpoint $M$ of $P$ and $Q$.

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