
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 located in the first and fourth quadrants (including the origin), and the x-coordinate of any point on curve C is less than its distance to point F(1,0) by 1.
(I) Find the equation of curve C;
(II) Find the coordinates of the point on curve C that has the minimum distance to the line x+y+4=0.

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