
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 that curve C is the locus of a moving point whose distances to two fixed points A(1, 0) and B(4, 0) have a ratio of $\frac{1}{2}$.

(1) Find the equation of curve C;  
(2) Find the minimum and maximum values of the distance $d$ from points on curve C to the line $l: x - y + 3 = 0$.

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