
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 the equation C: $x^2+y^2-4x-4y+a=0$  
(1) If equation C represents a circle, find the range of values for the real number $a$;  
(2) For equation C, when $a=-17$, find the equation of the tangent line that passes through the point $(7, -6)$ and is tangent to circle C;  
(3) If the circle C from (1) intersects with line $l: 2x-y-3=0$ at points A and B, and $OA \perpendicular OB$ (where O is the origin), find the value of the real number $a$.

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