
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 A $(1, -2)$ and B $(-4, -2)$, consider the following four curves:
① $4x+2y=3$, ② $x^2+y^2=3$,
③ $x^2+2y^2=3$, ④ $x^2-2y=3$.
Among these curves, there exists at least one where point P can be found such that $|PA| = |PB|$. Fill in the blank with the correct proposition number(s).

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