
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 $$\overrightarrow {m}=( \sqrt {3}\sin \frac {x}{4}, 1)$$, $$\overrightarrow {n}=(\cos \frac {x}{4}, \cos^{2} \frac {x}{4})$$, let $$f(x)= \overrightarrow {m}\cdot \overrightarrow {n}$$.
(1) If $f(x)=1$, find the value of $$\cos(x+ \frac {\pi}{3})$$;
(2) In an acute triangle $\triangle ABC$, where the sides opposite angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and it satisfies $(2a-c)\cos B=b\cos C$, find the range of values for $f(2A)$.

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