
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 $f(x)=2\cos^2x-\sin(2x-\frac{7\pi}{6})$,
(Ⅰ) Find the maximum value of the function $f(x)$, and write down the set of values for $x$ for which $f(x)$ attains its maximum value;
(Ⅱ) In triangle $ABC$, where the sides opposite angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively, if $f(A)=\frac{3}{2}$ and $b+c=2$, find the minimum value of the real number $a$.

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