
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 the equation $(x-2)^2 + y^2 = 1$, and a moving point Q on the line $y=x$, the tangents QA and QB from Q to circle M are tangent to the circle at points A and B, respectively.  
(1) If the coordinates of point Q are (0, 0), find the equations of the tangents QA and QB.  
(2) If the coordinates of point Q are $(t, t)$, where $t \in \mathbb{R}$, find the equation of line AB.

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