
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
Find the equation of the straight line $l$ that passes through the point $(1,0)$ and intersects with two parallel lines $l_1: 3x + y - 6 = 0$ and $l_2: 3x + y + 3 = 0$ such that the segment between $l_1$ and $l_2$ cut by $l$ has a length of $\frac{9\sqrt{10}}{10}$.

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