
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 two points $M(1,\frac{5}{4}), N(-4,-\frac{5}{4})$, consider the following curve equations:

1. $x^2+y^2=4$;
2. $\frac{x^2}{2}+y^2=1$;
3. $\frac{x^2}{2}-y^2=1$.

Among the above curves, the equations of all curves that have a point $P$ satisfying $|MP|=|NP|$ are (write the serial number only).

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