
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 $f(x)=a\sin (2x- \frac{\pi}{3})+b$ $(x\in \mathbb{R})$  
$(1)$ Find the equation of the axis of symmetry for the function $f(x)$;  
$(2)$ If $a > 0$ and $x\in\left[0, \frac{\pi}{2}\right]$, the minimum value of $f(x)$ is $-2$ and the maximum value is $\sqrt{3}$. Find the values of the real numbers $a$ and $b$.

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