
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
The set of real numbers $x$ that satisfy the inequality $|x-A| < B$ (where $A \in \mathbb{R}, B > 0$) is called the $B$-neighborhood of $A$. If the $a+b$-neighborhood of $a+b-t$ (where $t$ is a positive constant) is an interval symmetric about the origin, then the minimum value of $a^2 + b^2$ is __________.

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