
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 plane rectangular coordinate system $xOy$, given points $M(0,-1)$ and $N(2,5)$.  
$(1)$ If $M$ and $N$ are two vertices of a square on one side, find the equations of the two lines passing through vertex $M$.  
$(2)$ If $M$ and $N$ are two vertices of a square on one diagonal, find the equation of the other diagonal line of the square.

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