
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 $f(x)=\cos x( \sqrt {3}\cos x-\sin x)- \sqrt {3}$  
$(1)$ Find the smallest positive period of the function $f(x)$ and the equation of the axis of symmetry of the graph.  
$(2)$ Find the intervals where the function $f(x)$ is increasing.  
$(3)$ Find the minimum value of the function $y=f(x)$ in the interval $\left[0, \dfrac {\pi}{2}\right]$ and the value of $x$ for which $y=f(x)$ attains this minimum value.

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