
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
In the Cartesian coordinate system, the point $P(6-3m, m+1)$ is given.<br/>$(1)$ If the distance from $P$ to the $y$-axis is $2$, find the value of $m$;<br/>$(2)$ If the horizontal and vertical coordinates of point $P$ are equal, find the coordinates of point $P$;<br/>$(3)$ Under the condition in $(2)$, there is a point $Q$ in the second quadrant such that $PQ$ <span class="special-symbol">∥</span> $x$-axis, and $PQ=3$, find the coordinates of point $Q$.

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