
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 $f(x)=\sin x+ \sqrt {3}\cos x$ $(x\in\mathbb{R})$.
(Ⅰ) Find the period and maximum value of the function $f(x)$;
(Ⅱ) If $f\left(A+ \frac {\pi}{6}\right)= \frac {2}{3}$, find the value of $\cos 2A$.

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