
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 $y=x^{2}-6x+5$ intersects with the coordinate axes at points that all lie on a circle $C$.  
(Ⅰ) Find the equation of circle $C$;  
(Ⅱ) If circle $C$ intersects with the line $x-y+a=0$ at points $A$ and $B$, and $CA \perp CB$, find the value of $a$.

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