
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 the equation of line $l$ as $(a+1)x + y - 2 - a = 0, (a \in \mathbb{R})$.

(1) Find the equation of line $l$ when the distance from point $A(5, 3)$ to line $l$ is maximum.

(2) If line $l$ intersects the positive semi-axes of the $x$ and $y$ axes at points $M$ and $N$ respectively, find the equation of line $l$ when the area of $\triangle OMN$ is minimum.

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