
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 coordinate origin, $\overrightarrow{OA}=(\sin \alpha,1)$, $\overrightarrow{OB}=(\cos \alpha,0)$, $\overrightarrow{OC}=(-\sin \alpha,2)$, and point $P$ satisfies $\overrightarrow{AB}=\overrightarrow{BP}$.
(I) Define function $f(\alpha)=\overrightarrow{PB}\cdot\overrightarrow{CA}$, find the smallest positive period of function $f(\alpha)$;
(II) 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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