
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 C with its center at (1, 2), the chord intercepted by the line \( l: 2x - y - 5 = 0 \) has a length of \( 4\sqrt{5} \).

(Ⅰ) Find the equation of circle C.
(Ⅱ) Let P be a point on line l with an abscissa of -4. Find the equation of the tangent line to the circle that passes through point P.

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