
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
The following propositions are about conic sections:

1. Let $A$ and $B$ be two fixed points, and $P$ be a moving point. If $|PA| + |PB| = 8$, then the trajectory of the moving point $P$ is an ellipse;
2. Let $A$ and $B$ be two fixed points, and $P$ be a moving point. If $|PA| = 10 - |PB|$, and $|AB| = 8$, then the maximum value of $|PA|$ is $9$;
3. Let $A$ and $B$ be two fixed points, and $P$ be a moving point. If $|PA| - |PB| = 6$, then the trajectory of the moving 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.

Determine the sequence numbers of the true propositions.

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