
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
Consider a linear function \( f(x) = ax + b \) defined only for \( \frac{1}{4} \le x \le \frac{3}{4} \), where a and b are constants with \( a > 0 \). Determine the range of \( f \) in terms of \( a \) and \( b \).

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