
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
If $A$ and $B$ are two distinct points on the parabola $y^2=4x$, and the perpendicular bisector of chord $AB$ (which is not parallel to the y-axis) intersects the x-axis at point $P$, then chord $AB$ is called a "related chord" of point $P$;  
(Ⅰ) Find the x-coordinate of the midpoint of the "related chord" of point $P(4,0)";  
(Ⅱ) Find the maximum length of all "related chords" of point $P(4,0)".

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