
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 the line $y=ax+1$ and the parabola $y^2=4x$ (where F is the focus of the parabola) intersect at points A and B.  
(Ⅰ) Find the range of the real number $a$;  
(Ⅱ) Find the value of the real number $a$ such that the circle with diameter AB passes through point F.

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