
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 "distance" between two sets of numbers A and B as the minimum value of $|a-b|$, where $a \in A, b \in B$. If $A=\{y|y=2x-1, x \in \mathbb{R}\}$ and $B=\{y|y=x^2+1, x \in \mathbb{R}\}$, then the "distance" between A and B is

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