
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 system $xoy$, $A$, $B$, and $C$ are three distinct points on the circle $x^2+y^2=1$. If there exist positive real numbers $\lambda$ and $\mu$ such that $$\overrightarrow{OC}=\lambda \overrightarrow{OA}+\mu \overrightarrow{OB},$$ calculate the range of values for $\lambda^2+(\mu-3)^2$.

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