
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 a curve C on the right side of the y-axis, the difference between the distance from each point on C to the point F(1, 0) and its distance to the y-axis is always 1.
(Ⅰ) Find the equation of curve C;
(Ⅱ) Determine whether there exists a positive number m, such that for any line passing through point M(m, 0) and intersecting curve C at two points A and B, the inequality $$\overrightarrow {FA}\cdot \overrightarrow {FB} < 0$$ always holds. If such m exists, find the range of m; if not, explain why.

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