
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, and vectors $\overrightarrow{OA}=(\sin α,1)$, $\overrightarrow{OB}=(\cos α,0)$, $\overrightarrow{OC}=(-\sin α,2)$, and point $P$ satisfies $\overrightarrow{AB}=\overrightarrow{BP}$.
(I) Denote function $f(α)=\overrightarrow{PB} \cdot \overrightarrow{CA}$, find the minimum positive period of function $f(α)$;
(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}
user