
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 $\overrightarrow{m}=( \sqrt {3}\cos x,-1)$, $\overrightarrow{n}=(\sin x,\cos ^{2}x)$.
(1) Find the dot product of $\overrightarrow{m}$ and $\overrightarrow{n}$ when $x= \dfrac {\pi}{3}$;
(2) If $x\in[0, \dfrac {\pi}{4}]$, and $\overrightarrow{m}\cdot \overrightarrow{n}= \dfrac { \sqrt {3}}{3}- \dfrac {1}{2}$, find the value of $\cos 2x$.

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