
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 $P(-1, 1)$, it is intersected by two parallel lines $l_1: x + 2y - 5 = 0$ and $l_2: x + 2y - 3 = 0$ such that the midpoint $M$ of the segment $M_1M_2$ formed by the intersections lies on the line $l_3: x - y - 1 = 0$. Find the equation of line $l$.

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