
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 a radius of 5 whose center is on the x-axis and the x-coordinate of the center is an integer. The circle is tangent to the line $4x+3y-29=0$.  
(1) Find the equation of the circle;  
(2) Let the line $ax-y+5=0$ ($a>0$) intersect the circle at points A and B. Find the range of the real number $a$.

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