
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]$ . What are the domain and range, respectively, of the function  $ g$  defined by  $ g(x)=1-f(x+1)$ ?

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