
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 line $l$ that passes through point $M(1,1)$, and intersects the positive semi-axes of the $x$-axis and $y$-axis at points $A$ and $B$ respectively, with $O$ being the origin of the coordinate system. Find:
1. The equation of line $l$ when the sum of the distances $|OA|$ and $|OB|$ is minimal;
2. The equation of line $l$ when the sum of the squares of distances $|MA|^2$ and $|MB|^2$ is minimal.

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