
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
Which of the following statements is correct?

1. In $\triangle ABC$, if $\sin A = \cos B$, then $\triangle ABC$ is a right triangle.
2. If $|\vec{a}| = 1$ and $|\vec{b}| = 2$, then the maximum value of $|\vec{a} + \vec{b}| + |\vec{a} - \vec{b}|$ is $2\sqrt{5}$.
3. In $\triangle ABC$, if $2\sin A \sin B < -\cos(2B + C)$, then $\sin^3 B + \sin^3 A - \sin^3 C < 0$.
4. In $\triangle ABC$, if $\sin^4 B + \sin^4 A + \sin^4 C + \sin^2 A \sin^2 B = 2\sin^2 A \sin^2 C + 2\sin^2 B \sin^2 C$ and $C$ is an acute angle, then the maximum value of $\sin A + \sin B$ is $\sqrt{3}$.

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