
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 two lines $l_1: (3+m)x + 4y = 5 - 3m$ and $l_2: 2x + (5+m)y = 8$ are perpendicular, find the value of the real number $m$. If the line $3x + 4y - 3 = 0$ is parallel to the line $6x + my + 14 = 0$, find the distance $d$ between them.

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