
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 $P(2m+4, m-1)$, find the coordinates of point $P$ under the following conditions:<br/>$(1)$ Point $P$ lies on the $y$-axis;<br/>$(2)$ The distance from point $P$ to the $y$-axis is $6$;<br/>$(3)$ Point $P$ lies in the third quadrant and is equidistant from both coordinate axes.

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