
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
If the ellipses $C_1: \frac{x^2}{a_1^2} + \frac{y^2}{b_1^2} = 1 \ (a_1 > 0, b_1 > 0)$ and $C_2: \frac{x^2}{a_2^2} + \frac{y^2}{b_2^2} = 1 \ (a_2 > b_2 > 0)$ have the same foci, and $a_1 > a_2$, then from the following four conclusions, the correct ones are: _______  
1. Ellipse $C_1$ and ellipse $C_2$ definitely do not have any common points;    
2. $\frac{a_1}{a_2} > \frac{b_1}{b_2}$;  
3. $a_1^2 - a_2^2 = b_1^2 - b_2^2$;  
4. $a_1 - a_2 < b_1 - b_2$.

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