
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 $f(x)=\sin x+a\cos x(x∈R)$ whose one symmetric axis is $x=- \frac {π}{4}$.
(I) Find the value of $a$ and the monotonically increasing interval of the function $f(x)$;
(II) If $α$, $β∈(0, \frac {π}{2})$, and $f(α+ \frac {π}{4})= \frac { \sqrt {10}}{5}$, $f(β+ \frac {3π}{4})= \frac {3 \sqrt {5}}{5}$, find $\sin (α+β)$

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