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