
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 $f(x)=(\sin^2x+\sin x\cos x)+2\sin \left(\frac{\pi}{4}-x\right)\cdot \cos \left(\frac{\pi}{4}-x\right)$

(I) If $\alpha =\frac{\pi}{3}$, find the value of $f(\alpha)$;

(II) If $x\in\left[\frac{\pi}{12},\frac{\pi}{4}\right]$, find the range of $f(x)$.

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