
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 circle $C$ with equation $(x-1)^2+y^2=4$ that contains a point $P(2,1)$. A line $l$ passes through point $P$ and intersects the circle $C$ at points $A$ and $B$.
1. If the length of chord $AB$ is maximized, find the equation of line $l$.
2. If $\overrightarrow{CA} \cdot \overrightarrow{CB} = 0$, find the equation of line $l$.

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