
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 $P(2, 3)$, and is intercepted by two parallel lines $l_1: 3x + 4y - 7 = 0$ and $l_2: 3x + 4y + 8 = 0$, the length of the segment cut off by these lines is $d$.
(1) Find the minimum value of $d$ and the equation of the line.
(2) Find the value of $d$ when line $l$ is parallel to the $x$-axis.

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