
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
A point A(a, 0), where a > 0, is given on a line with an inclination angle of 30°. This line is tangent to a circle O: $x^2 + y^2 = r^2$, where r > 0, at point B. If the distance between points A and B is $\sqrt{3}$, determine the area of triangle OAB.

A) $\frac{1}{2}$
B) $\frac{\sqrt{3}}{2}$
C) $1$
D) $2$

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