
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 $$f(x)=2\cos^{2}(x- \frac {\pi}{4})- \sqrt {3}\cos2x+1,$$  
(1) Find the equation of the axis of symmetry for the graph of $f(x)$;  
(2) Find the maximum and minimum values of $f(x)$ on the interval $$\left[ \frac {\pi}{4}, \frac {\pi}{2}\right];$$  
(3) If for any real number $x$, the inequality $|f(x)-m|<2$ always holds for $x\in\left[ \frac {\pi}{4}, \frac {\pi}{2}\right]$, find the range of the real number $m$.

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