
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 $\overrightarrow{m}=(\cos x,-\sin x)$ and $\overrightarrow{n}=(\cos x,\sin x-2 \sqrt {3}\cos x)$, where $x\in R$, let $f(x)= \overrightarrow{m}\cdot \overrightarrow{n}$.
(1) Find the smallest positive period of function $f(x)$ and the equation of the axis of symmetry of its graph;
(2) Find the range of function $f(x)$ in the interval $\left[-\dfrac{\pi}{12},\dfrac{\pi}{2}\right]$.

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