
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 $f(x) = \sin x \cos x - \sin^2 x + \frac{1}{2}$,

(Ⅰ) Determine the intervals where $f(x)$ is monotonically increasing;

(Ⅱ) In the triangle $ABC$, let $a$, $b$, and $c$ be the lengths of the sides opposite to angles $A$, $B$, and $C$ respectively, and let it be given that $b\cos 2A = b\cos A - a\sin B$ with $0 < A < \frac{\pi}{2}$. Find the range of values for $f(B)$.

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