
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
In the Cartesian coordinate plane, $O$ is the origin, $A(1,1)$, $B(2,0)$, and $|\overrightarrow{OC}| = 1$.
(1) Find the angle between $\overrightarrow{OA}$ and $\overrightarrow{OB}$;
(2) If $\overrightarrow{OC}$ is perpendicular to $\overrightarrow{OA}$, find the coordinates of point $C$;
(3) Find the range of values for $|\overrightarrow{OA} + \overrightarrow{OB} + \overrightarrow{OC}|$.

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