
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 $\overrightarrow{a}=(1,\sqrt{3})$, $\overrightarrow{b}=(\cos x,\sin x)$, and the function $f(x)=\overrightarrow{a}\bullet \overrightarrow{b}-1$.

(1) Find the set of all $x$ such that $f(x)=0$;

(2) If $x\in [0,\dfrac{\pi }{2}]$, find the monotonic intervals and the extreme values of $f(x)$.

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