
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 function $f(x)=a\sin x\cos x-\sqrt{3}a\cos^{2}x+\frac{\sqrt{3}}{2}a+b(a\neq 0)$.

(1) Find the equation of the axis of symmetry of the graph of the function $f(x)$ for $x\in R$;

(2) If the minimum value of the function $f(x)$ is $2$ and the maximum value is $4$, find the values of the real numbers $a$ and $b$.

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