
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 point A(4, m) lies on the parabola $y^2=2px$ (with $p>0$), and the distance from point A to the focus F of the parabola is 5,
(Ⅰ) Find the equation of the parabola and the value of m;
(Ⅱ) If $m>0$, find the equation of line L that passes through point A and intersects the parabola at exactly one point.

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