
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]


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Let \( f \) be a function with domain \([0,2]\) and range \([0,1]\). Define a new function \( g \) by the formula:
\[ g(x) = 1 - f\left(\frac{x}{2} + 1\right) \]
Determine the domain and range of \( g(x) \), and express your answer as an ordered quadruple \( (a, b, c, d) \).

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