
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 that $O$ is the origin of coordinates, and the vectors $\overrightarrow{OA}=(\sin \alpha,1)$, $\overrightarrow{OB}=(\cos \alpha,0)$, $\overrightarrow{OC}=(-\sin \alpha,2)$. Point $P$ satisfies $\overrightarrow{AB}= \overrightarrow{BP}$  
$(1)$ Let the function $f(\alpha)= \overrightarrow{PB}\cdot \overrightarrow{CA},\alpha\in\left(- \frac {\pi}{8}, \frac {\pi}{2}\right)$, discuss the monotonicity of the function $f(\alpha)$ and find its range;  
$(2)$ If points $O$, $P$, and $C$ are collinear, find the value of $|\overrightarrow{OA}+ \overrightarrow{OB}|$.

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