
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 the following statements:
① If $\alpha$ and $\beta$ are both in the first quadrant, and $\alpha > \beta$, then $\sin\alpha > \sin\beta$.
② The function $f(x) = \sin(2x - \frac{\pi}{3})$ is increasing in the interval $[0, \frac{5\pi}{12}]$.
③ A center of symmetry for the function $f(x) = \cos(2x + \frac{\pi}{3})$ is $(-\frac{\pi}{6}, 0)$.
④ Define $\min\{a, b\} = \begin{cases} a, & \text{if } a \leq b \\ b, & \text{if } a > b \end{cases}$. If $f(x) = \min\{\sin x, \cos x\}$, then the range of $f(x)$ is $[-1, \frac{\sqrt{2}}{2}]$.

Which of the statements are correct? Fill in the blank with the numbers of the correct statements.

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