
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 $l: 2x + y + 4 = 0$ and the circle $C: x^2 + y^2 + 2x - 4y + 1 = 0$, let the two intersection points be A and B.

(1) Find the coordinates of A and B.

(2) Point D is on the x-axis, such that triangle ABD is an isosceles triangle. Find the coordinates of point D.

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