
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
Two parallel lines \( l_{1} \) and \( l_{2} \) have a distance \( d \) between them. They pass through the points \( M(-2, -2) \) and \( N(1, 3) \) respectively, and rotate around \( M \) and \( N \) while remaining parallel. Determine the equations of the lines \( l_{1} \) and \( l_{2} \) when \( d \) reaches its maximum value.

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