
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
Define the solution set of the inequality $|x-A| < B$ ($A\in\mathbb{R}, B > 0$) as the $B$-neighborhood of $A$. If the $a+b$-neighborhood of $a+b-3$ is the interval $(-3,3)$, then the minimum value of $a^{2}+b^{2}$ is ______.

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