
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 that line $l$ intersects circle $M:{x}^{2}+{y}^{2}=4$ at two points $A,B$. If the midpoint of segment $AB$ is $P(1,1)$, find the equation of line $l$ and the length of the chord cut by line $l$ on circle $M$.

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