
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 domain of the function $f\left( x \right)=\frac{1}{\ln \left( x+1 \right)}+\sqrt{4-{{x}^{2}}}$ is given by the set of all real numbers x for which the functions $\ln \left( x+1 \right)$ and $\sqrt{4-{{x}^{2}}}$ are both defined. Determine the domain of the function $f\left( x \right)=\frac{1}{\ln \left( x+1 \right)}+\sqrt{4-{{x}^{2}}}$.

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