
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 a domain \([0,3]\) and range \([0,1]\). Define a new function by
\[ g(x) = 1 - 2f(x + 2). \]
Determine the domain and range of \(g(x)\), and provide the results as the ordered quadruple \((a, b, c, d)\).

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