
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
A function $f$ has domain $[0,2]$ and range $[0,1]$. Define another function by
\[ g(x) = 1 - f(x^2 + 1) \]
Determine the domain and range of $g(x)$ and provide them as an ordered quadruple $(a, b, c, d)$.

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