
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 $a>0$, $b>0$, and circle $C: (x-2)^2+(y+1)^2=5$ is symmetric with respect to the line $ax-by-1=0$, the minimum value of $\frac{3}{b}+ \frac{2}{a}$ is \_\_\_\_\_\_.

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