
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
Among the following propositions about conic sections:  
① Given two fixed points A and B, and a moving point P, if $|PA| + |PB| = 8$, then the trajectory of point P is an ellipse;  
② Given two fixed points A and B, and a moving point P, if $|PA| = 10 - |PB|$, and $|AB| = 8$, then the maximum value of $|PA|$ is 9;  
③ Given two fixed points A and B, and a moving point P, if $|PA| - |PB| = 6$, then the trajectory of point P is a hyperbola;  
④ The hyperbola $\frac{x^{2}}{16} - \frac{y^{2}}{10} = 1$ and the ellipse $\frac{x^{2}}{30} + \frac{y^{2}}{4} = 1$ have the same foci.  
The numbers of the true propositions are __________.

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