
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
Points M and N are two moving points on a parabola E. The distance from M to the point (2, 0) is 1 less than its distance to the line \( x + 3 = 0 \). Point O (not coinciding with M or N) is the origin, and OM is perpendicular to ON.
(Ⅰ) Find the standard equation of the parabola E;
(Ⅱ) Determine whether there exists a fixed point on the x-axis which always lies on line MN. If such a point exists, find its coordinates; if not, explain why.

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