
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 circle $C_{1}$: $x^{2}+y^{2}+2ax+a^{2}-4=0$, where $a\in \mathbb{R}$, and circle $C_{2}$: $x^{2}+y^{2}-2by-1+b^{2}=0$, where $b\in \mathbb{R}$, have only one common tangent line. Find the minimum value of $a+b$.

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