
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 the line $l$ passes through point $P(3, 1)$ and is intersected by two parallel lines $l_1: x + y + 1 = 0$ and $l_2: x + y + 6 = 0$ such that the length of the segment between the lines is 5. Find the equation of line $l$.

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