
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 the function $f(x)= \begin{cases} \frac {x+1}{x^{2}}, & x < -1 \\ \ln (x+2), & x\geqslant -1\end{cases}$ and $g(x)=x^{2}-2x-4$. Let $b$ be a real number, if there exists a real number $a$ such that $f(a)+g(b)=1$ holds, then the range of values for $b$ is \_\_\_\_\_\_.

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