
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
The line $y=x+n$ intersects with the line $y=mx+3n$ (where $m$ is a constant, $m\neq 0$, and $m\neq 1$) at point $A$. When the value of $n$ changes, the distance from point $A$ to the line $y=\frac{3}{4}x-3$ is always a constant. Determine the value of $m$.

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