
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 $f(x)=2\sin ^{2}(x+ \dfrac {\pi}{4})- \sqrt {3}\cos 2x$, where $x\in[\dfrac {\pi}{4}, \dfrac {\pi}{2}]$. Let $x=\alpha$ when $f(x)$ reaches its maximum value.
(1) Find the maximum value of $f(x)$ and the value of $\alpha$;
(2) In $\triangle ABC$, angles $A$, $B$, and $C$ correspond to sides $a$, $b$, and $c$ respectively, where $A=\alpha- \dfrac {\pi}{12}$, and $\sin B\sin C=\sin ^{2}A$. Find the value of $b-c$.

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