
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 points $A(\sin\theta, 1)$, $B(\cos\theta, 0)$, $C(-\sin\theta, 2)$, and $\overset{→}{AB}=\overset{→}{BP}$.
(I) Consider the function $f\left(\theta\right)=\overset{→}{BP}\cdot\overset{→}{CA}$, $\theta\in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$, discuss the monotonicity of the function and find its range.
(II) If points $O$, $P$, $C$ are collinear, find the value of $\left|\overset{→}{OA}+\overset{→}{OB}\right|$.

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