
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 $$f(x)=2\sin^{2}\left( \frac {\pi}{4}+x\right)- \sqrt {3}\cos2x$$.
(1) Find the interval of monotonic decrease for the function $f(x)$;
(2) If the equation $f(x)=a$ has two distinct real solutions in the interval $$x\in\left[ \frac {\pi}{4}, \frac {\pi}{2}\right]$$, find the sum of these two solutions;
(3) If the inequality $|f(x)-m|<2$ always holds in the interval $$x\in\left[ \frac {\pi}{4}, \frac {\pi}{2}\right]$$, find the range of the real number $m$.

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