
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 the function $$f(x)=2\cos(2x+ \frac {\pi}{3})-2\cos x+1$$.
(1) Try to express the function $f(x)$ in the form of $f(x)=A\sin(\omega x+\varphi)+B$ ($\omega>0$), and find the center of symmetry of this function;
(2) If in an acute triangle $\triangle ABC$, the sides opposite angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and $f(A)=0$, find the range of values for $\frac {b}{c}$.

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