
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 the function \( f(x) = ax^2 + bx + c + d\sin(kx) \) where \( a > 0, k > 0 \) and \( d \) is a real number. What is the least value of the function?
A) \( \frac{-b^2 + 4ac}{4a} \)
B) \( \frac{-b^2 + 4ac - 4ad}{4a} \)
C) \( \frac{-b^2 + 4ac + 4ad}{4a} \)
D) \( \frac{-b^2 + 2ac}{4a} \)

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