
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 the center coordinates (2, 2), and it is tangent to the line $3x+4y-9=0$.
(1) Find the equation of circle C;
(2) Determine whether there exists a real number $a$ such that circle C intersects with the line $x-y+a=0$ at points A and B, and satisfies $\angle AOB=90^\circ$. If it exists, find the value of $a$; if not, explain why.

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