
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
Among the following statements, the correct ones are \_\_\_\_\_\_\_.

(1) If $\cos θ < 0$, then $θ$ is an angle in the second or third quadrant;

(2) The line $x=\frac{π}{2}+2kπ, k \in \mathbb{Z}$ is the axis of symmetry for the sine curve;

(3) If the terminal sides of angles $α$ and $β$ are symmetric about the $y$-axis, then $α+β=(2k-1)π, k \in \mathbb{Z}$;

(4) $y=\tan x$ is an increasing function over its domain;

(5) The function $y=\sqrt{\cos x - 1}$ is an even function.

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