
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 plane Cartesian coordinate system \( x O y \), let \( A, B, C \) be distinct points on the circle \( x^{2}+y^{2}=1 \). If there exist positive real numbers \( \lambda \) and \( \mu \) such that \( \overrightarrow{O C}=\lambda \overrightarrow{O A}+\mu \overrightarrow{O B} \), what is the range of values of \( (\lambda-1)^{2}+(\mu-3)^{2} \)?

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