
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 with radius 5 whose center C is on the x-axis, and the x-coordinate of the center C is an integer. The circle C is tangent to the line $4x+3y-33=0$.  
(1) Find the equation of circle C;  
(2) Suppose the line $ax-y-7=0$ intersects circle C at points A and B, and $CA \perp CB$, find the value of the real number $a$.

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