
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 the point F(0, 1) and its distance to the x-axis is always 1.  
(1) Find the equation of curve C;  
(2) Suppose the line $y=kx+m$ ($m>0$) intersects curve C at points A and B. If for any $k \in \mathbb{R}$, $\overrightarrow{FA} \cdot \overrightarrow{FB} < 0$, find the range of values for $m$.

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