
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
Shift all points on the curve $C$: $y=\sin \left( \frac {3\pi}{4}-x \right) \cdot \cos \left(x+ \frac {\pi}{4}\right)$ to the right by $a(a > 0)$ units to get the curve $C'$, and the curve $C'$ is centrally symmetric about the point $(0,0)$. When $x\in\left[ \frac {b+1}{8}\pi, \frac {b+1}{4}\pi \right]$ ($b$ is a positive integer), the slope of the line passing through any two points on the curve $C'$ is always less than zero, then the value of $b$ is $\boxed{\text{D: }1\text{ or }2}$.

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