
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 line $l: 4x+3y-8=0$ passes through the center of the circle $C: x^2+y^2-ax=0$ and intersects circle $C$ at points A and B, with O as the origin.
(I) Find the equation of circle $C$.
(II) Find the equation of the tangent to circle $C$ at point $P(1, \sqrt {3})$.
(III) Find the area of $\triangle OAB$.

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