
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 coordinates of point $P$ are $\left(n+3,2-3n\right)$.  
$(1)$ If the point is in the fourth quadrant and the distance from point $P$ to the $x$-axis is 1 greater than the distance to the $y$-axis, find the coordinates of point $P$.  
$(2)$ Given that point $Q\left(n,-4\right)$, when $PQ$ is parallel to the $x$-axis, find the length of $PQ$.

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