
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 number of correct statements among the following is ______.

(1) If the slope of a line is $\tan \alpha$, then its inclination angle is $\alpha$.

(2) Lines that do not pass through the origin can all be represented by $\dfrac{x}{a} + \dfrac{y}{b} = 1$.

(3) The equation of one of the axes of symmetry for the function $y=2\sin \alpha +2\cos \alpha$ is $x=\dfrac{\pi }{4}$.

(4) The range of the inclination angle for the line $x\cos \alpha + \sqrt{3}y +2=0$ is $\left[\begin{matrix}0, \dfrac{\pi}{6}\end{matrix}\right]\cup\left[\begin{matrix} \dfrac{5\pi}{6},\pi\end{matrix}\right]$.

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