
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
If \( g(x) \) is a function defined only for \( -1 \le x \le 2 \), and \( g(x) = ax^2 + bx + c \) for constants \( a, b, \) and \( c \) where \( a > 0 \), then what is the range of \( g \) in terms of \( a, b, \) and \( c \)? Express your answer in interval notation.

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