
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 two circles $C_{1}$: $\left(x-a\right)^{2}+y^{2}=1$ and $C_{2}$: $x^{2}+y^{2}-2by+b^{2}-4=0$ have exactly three common tangents, then the range of $a^{2}+b^{2}-6a-8b$ is ____.

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