
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 vectors $\overrightarrow{a}=(\sin x, \sqrt{3}\cos x)$ and $\overrightarrow{b}=(\cos x, -\cos x)$, the function $f(x) = \overrightarrow{a} \cdot \overrightarrow{b} + \frac{\sqrt{3}}{2}$:  
(1) Find the equation of the axis of symmetry for the graph of the function $y = f(x)$.  
(2) Find the maximum and minimum values of the function $f(x)$ on the interval $\left [0, \frac{\pi}{2} \right]$.

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