
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 a Cartesian coordinate system, \( A(1,2) \), \( B(3,0) \), and \( P \) are points on the circle \( (x-3)^{2}+(y-2)^{2}=1 \). Suppose
$$
\overrightarrow{O P}=\lambda \overrightarrow{O A}+\mu \overrightarrow{O B} \quad (\lambda, \mu \in \mathbf{R}).
$$

Find the minimum value of \( 11\lambda + 9\mu \).

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