
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 $|x-A| < B$ ($B > 0$, $A \in \mathbb{R}$) is called the $B$-neighborhood of $A$. If the $a+b$-neighborhood of $a+b-2$ is an interval symmetric about the origin, then the range of values for $\frac{1}{a} + \frac{4}{b}$ is \_\_\_\_\_\_.

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