
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 a circle M with its center on the x-axis and a radius of 1, the line $l: y=3x-1$ is intersected by circle M, producing a chord of length $\frac{2\sqrt{15}}{5}$, and the center of circle M is below line $l$.
(Ⅰ) Find the equation of circle M;
(Ⅱ) Let A(0, t), B(0, t+4) (-3≤t≤-1), and draw tangents to circle M from points A and B, intersecting at point C. Find the maximum and minimum values of the area $S$ of triangle ABC thus formed.

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