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

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