
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
In the Cartesian coordinate system xOy, the curve $y = x^2 - 6x + 1$ intersects with the coordinate axes all on circle C.  
(1) Find the equation of circle C;  
(2) If circle C intersects with the line $x - y + a = 0$ at points A and B, and $OA \perpendicular OB$, find the value of $a$. (13 points)

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