
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 that the vector $\overrightarrow{a}=(1, \cos \frac{x}{2})$ and the vector $\overrightarrow{b}=(\sqrt{3}\sin \frac{x}{2}+\cos \frac{x}{2}, y)$ are collinear, and there is a function $y=f(x)$,
(Ⅰ) If $f(x)=1$, find the value of $\cos(\frac{2\pi}{3} - 2x)$;
(Ⅱ) In $\triangle ABC$, where the sides opposite angles A, B, C are a, b, c respectively and satisfy $2a\cos C + c = 2b$, find the range of values for the function $f(B)$.

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