
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
Given a triangle $\triangle ABC$, there are the following propositions:

1. If $\sin 2A = \sin 2B$, then $\triangle ABC$ is an isosceles triangle.
2. If $\sin A = \cos B$, then $\triangle ABC$ is a right triangle.
3. If $\sin^2 A + \sin^2 B + \cos^2 C < 1$, then $\triangle ABC$ is an obtuse triangle.

Determine the sequence number(s) of the correct proposition(s). (Fill in all the correct ones you find.)

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