
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
Given the function \( f(x) = ax^2 + bx + c \) (where \( a \neq 0 \)) defined on the interval \(\left[-\frac{b}{2a}, \frac{2a - b}{2a}\right]\), and the function's minimum value is not \(\frac{4ac - b^2}{4a}\), what is the function's minimum value?

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