
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 that the center of circle C is at the origin O, and it is tangent to line $l\_1: x - y - 2\sqrt{2} = 0$.
(1) If a line perpendicular to line $l\_1$ intersects circle C at two distinct points P and Q, and a circle passing through the origin with PQ as the diameter, find the y-intercept of the line.
(2) Find the equation of the tangent line to circle C passing through point G(1, 3).

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