
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 point $M(m+3,2m-1)$, point $M$ is moved up by $4$ units to get point $N$.<br/>$(1)$ If the ordinate of point $N$ is $3$ greater than its abscissa, find the coordinates of point $M$;<br/>$(2)$ If the distance from point $M$ to the $x$-axis is $2$ and it lies in the fourth quadrant, find the coordinates of point $N$.

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