
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 moving point $P$ is on the line $l_1$: $3x-4y+1=0$, and the moving point $Q$ is on the line $l_2$: $6x+my+4=0$, and $l_1$ is parallel to $l_2$, find the minimum value of $|PQ|$.

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