
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 on the line $y=x+1$ and a radius of $\sqrt{2}$, and circle C passes through points P(5, 4) and Q(3, 6).
(1) Find the standard equation of circle C;
(2) Find the equation of the tangent line passing through point A(1, 0) and tangent to circle C.

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