
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 $f(x) = \begin{cases} \frac{2x+1}{x^{2}}, & x < -\frac{1}{2} \\ \ln(x+1), & x \geq -\frac{1}{2} \end{cases}$, and $g(x) = x^2 - 4x - 4$, if $f(a) + g(b) = 0$, then the range of values for $b$ is \_\_\_\_\_\_.

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