
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 vectors $\overrightarrow{a}=(\cos (x+ \frac {\pi}{8}),\sin ^{2}(x+ \frac {\pi}{8}))$ and $\overrightarrow{b}=(\sin (x+ \frac {\pi}{8}),1)$, and the function $f(x)=2 \overrightarrow{a}\cdot \overrightarrow{b}-1$.

(Ⅰ) Find the explicit expression of the function $f(x)$, and state the period and the coordinates of the symmetry center of the function $f(x)$.

(Ⅱ) Find the interval of monotonic increase for the function $y=f(- \frac {1}{2}x)$.

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