
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 $$f(x)=2\sin(wx+\varphi+ \frac {\pi}{3})+1$$ where $|\varphi|< \frac {\pi}{2}$ and $w>0$, is an even function, and the distance between two adjacent axes of symmetry of the function $f(x)$ is $$\frac {\pi}{2}$$.  
(1) Find the value of $$f( \frac {\pi}{8})$$.  
(2) When $x\in(-\frac {\pi}{2}, \frac {3\pi}{2})$, find the sum of the real roots of the equation $f(x)= \frac {5}{4}$.

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