
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 the following four propositions:  
① For the ellipse $\frac {x^{2}}{16} + \frac {y^{2}}{9} = 1$ with its left and right foci being $F_1$ and $F_2$ respectively, and $P$ is a point on the ellipse with $|PF_1|=3$, then $|PF_2|=1$;  
② For the hyperbola $C: \frac {y^{2}}{9} - \frac {x^{2}}{16} = 1$, the distance from its vertex to the asymptote is $\frac {12}{5}$;  
③ If $\bigodot C_1: x^2+y^2+2x=0$ and $\bigodot C_2: x^2+y^2+2y-1=0$, then these two circles have exactly 2 common tangents;  
④ If the line $l_1: a^2x-y+6=0$ and the line $l_2: 4x-(a-3)y+9=0$ are perpendicular to each other, then $a=-1$  
Among these, the correct propositions are \_\_\_\_\_\_ . (Fill in the numbers of all correct propositions)

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