
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
The correct statements among the following are __________  
(1) The function $f(x) = 4 \cos(2x + \frac{π}{3})$ has a symmetry center at $(-\frac{5π}{12}, 0)$;  
(2) In triangle $ABC$, $AB = 1$, $AC = 3$, and $D$ is the midpoint of $BC$, then $\vec{AD} \cdot \vec{BC} = 4$;  
(3) In triangle $ABC$, $A < B$ is the necessary and sufficient condition for $\cos 2A > \cos 2B$;  
(4) Defined $min\{a, b\} = \begin{cases} a, & \text{if } a \leq b \\ b, & \text{if } a > b \end{cases}$, given $f(x) = min\{\sin x, \cos x\}$, then the maximum value of $f(x)$ is $\frac{\sqrt{2}}{2}$.

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