
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 $M(1,\frac{5}{4})$ and $N(-4,-\frac{5}{4})$, determine the curve equations below:<br/>①$4x+2y-1=0$；②$x^{2}+y^{2}=3$；③${x}^{2}+\frac{{y}^{2}}{4}=1$；④${x}^{2}-\frac{{y}^{2}}{4}=1$.<br/>Find the numbers of the equations of curves that have a point $P$ satisfying $|PM|=|PN|$.

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