The relationship described in the first analogy is based on increasing intensity:
\[
\text{walk} \to \text{jog} \to \text{sprint}.
\]
This progression moves from low intensity (\text{walk}) to high intensity (\text{sprint}).
Similarly, in the second analogy:
\[
\text{bothered} \to \text{\_\_\_} \to \text{daunted}.
\]
Step 1: Analyze the terms.
"Bothered" indicates mild disturbance, and "daunted" represents a high level of emotional disturbance. The intermediate level is best represented by "fazed."
Step 2: Eliminate incorrect options.
(1) "phased" does not relate to emotional intensity.
(2) "phrased" is unrelated to emotions.
(4) "fused" does not fit the context.
Hence, (3) "fazed" aligns with the progression.
Final Answer:
\[
\boxed{\text{fazed}}
\]