
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
For $\triangle ABC$, the following propositions are given:  
(1) If $\sin 2A = \sin 2B$, then $\triangle ABC$ must be an isosceles triangle.  
(2) If $\sin A = \sin B$, then $\triangle ABC$ must be an isosceles triangle.  
(3) If $\sin^2 A + \sin^2 B + \cos^2 C < 1$, then $\triangle ABC$ must be an obtuse triangle.  
(4) If $\tan A + \tan B + \tan C > 0$, then $\triangle ABC$ must be an acute triangle.  
The correct proposition numbers are ____. (Fill in all the correct proposition numbers)

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