
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 the difference between the distance from any point on curve C to point F(0,1) and its distance to the x-axis is always 1:
1. Find the equation of curve C;
2. If line y=kx+m (m > 0) intersects curve C at points A and B, and for any k in R, the dot product of vectors FA and FB is always less than 0, find the range of m.

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