
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 that vertices \(A\) and \(C\) of triangle \(\triangle ABC\) are on the graph of the inverse proportional function \(y = \frac{\sqrt{3}}{x}\) (where \(x > 0\)), \(\angle ACB = 90^\circ\), \(\angle ABC = 30^\circ\), \(AB \perp x\)-axis, point \(B\) is above point \(A\), and \(AB = 6\). Determine the coordinates of point \(C\).

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