
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, given the point $P(m+1,2m-4)$, find the coordinates of point $P$ according to the following conditions:<br/>$(1)$ Point $P$ lies on the $x$-axis;<br/>$(2)$ Point $A(-5,2)$, the line segment $AP$ is parallel to the $y$-axis.

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