
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, for points $P$ and $Q$, the following definition is given: if the larger of the distances from point $P$ to the $x$-axis and $y$-axis is equal to the larger of the distances from point $Q$ to the $x$-axis and $y$-axis, then points $P$ and $Q$ are called "equidistant points." For example, the points $P(-2,5)$ and $Q(-5,-1)$ are equidistant points.  
$(1)$ Among the following points, those that are equidistant points of $(-3,7)$ are ______;  
① $(3,-7)$  
② $(2,9)$  
③ $(7,4)$  
$(2)$ Given that the coordinates of point $B$ are $(-4,2)$, and the coordinates of point $C$ are $(m-1,m)$, if points $B$ and $C$ are "equidistant points," find the coordinates of point $C$.

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