
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 $$f(x)= \frac { \sqrt {2}}{2}\sin(2x+ \frac {\pi}{4})+2$$, try to find:  
(1) The smallest positive period of the function $f(x)$ and the value of $x$ when $f(x)$ reaches its maximum value;  
(2) The interval of monotonic increase for the function $f(x)$;  
(3) If the equation $f(x)-m+1=0$ has a solution in $$x\in[0, \frac {\pi}{2}]$$, find the range of the real number $m$.

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