
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 $\triangle ABC$, there are four propositions:
1. If $\sin 2A = \sin 2B$, then $\triangle ABC$ is an isosceles triangle;
2. If $\sin B = \cos A$, then $\triangle ABC$ is a right triangle;
3. If $\sin^2A + \sin^2B > \sin^2C$, then $\triangle ABC$ is an acute triangle;
4. If $\dfrac{a}{\cos A} = \dfrac{b}{\cos B} = \dfrac{c}{\cos C}$, then $\triangle ABC$ is an equilateral triangle.

Among these, the correct propositions are __________.

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