
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
(The full score for this problem is 12 points) Given the function $f(x) = 2\cos x\sin\left( x + \frac{\pi}{4} \right) - \frac{\sqrt{2}}{2}$.
(Ⅰ) Determine the smallest positive period $T$ of the function $f(x)$;
(Ⅱ) Suppose the sides of triangle $ABC$, denoted as $a$, $b$, $c$, satisfy $b^2 = ac$, and the angle $B$ is opposite to side $b$. Determine the range of possible values for $\cos B$ and find the maximum value of $f(B)$.

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