
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 $\overrightarrow{m}=( \sqrt {3}\cos x,-1), \overrightarrow{n}=(\sin x,\cos ^{2}x)$, and function $f(x)= \overrightarrow{m}\cdot \overrightarrow{n}+ \frac {1}{2}$.
(1) If $x\in[0, \frac {π}{4}],f(x)= \frac { \sqrt {3}}{3}$, find the value of $\cos 2x$;
(2) In $\triangle ABC$, angles $A$, $B$, $C$ have corresponding opposite sides $a$, $b$, $c$, and satisfy $2b\cos A\leqslant 2c- \sqrt {3}a$, find the range of $f(B)$.

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