
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
Let the function $f(x) = (\sqrt{3}\sin\omega x + \cos\omega x)\cos\omega x - \frac{1}{2}$ ($\omega > 0$) have a minimum positive period of $4\pi$.

(Ⅰ) Find the interval of monotonic increase for the function $f(x)$.

(Ⅱ) Given that $a$, $b$, and $c$ are the lengths of the sides opposite to angles $A$, $B$, and $C$ in $\triangle ABC$, respectively, and satisfy $(2a-c)\cos B = b\cos C$, find the value of angle $B$ and the range of the function $f(A)$.

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