
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 $[0,3]$. Define a new function 
\[ g(x) = 3 - 2f(x+0.5). \]
Find 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}
user