
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
The line $l$ passing through point E($-1$,$0$) intersects the parabola C: $y^2=4x$ at points A and B. F is the focus of the parabola.
(1) If the x-coordinate of the midpoint of segment AB is 3, find the value of $|AF|+|BF|$.
(2) Find the range of values for $|AF|\cdot|BF|$.

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