
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 functions $$f(x)=2\sin^{2}(x+ \frac {π}{4})$$ and $$g(x)=1+\cos( \frac {x}{2}+ \frac {π}{4})$$, their graphs intersect at 9 distinct points, denoted as (x<sub>i</sub>, y<sub>i</sub>) (i=1, 2, …, 9), in the interval $$(\frac {π}{2}-m, \frac {π}{2}+m)$$. Calculate the value of $$\sum\limits_{i=1}^{9}(x_{i}+y_{i})$$.

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