
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
Triangle $OAB$ has vertices $O=(0,0)$, $B=(10,0)$, and point $A$ in the first quadrant, with $\angle ABO=90^\circ$ and $\angle AOB=30^\circ$. If point $A$ is rotated $90^\circ$ counterclockwise about $O$, find the coordinates of the image of $A$ after translating point $B$ 2 units up along the y-axis.
A) $\left(-\frac{10\sqrt{3}}{3}, 10\right)$
B) $\left(-\frac{10\sqrt{3}}{3}, 12\right)$
C) $\left(\frac{10\sqrt{3}}{3}, 10\right)$
D) $\left(\frac{10\sqrt{3}}{3}, 12\right)$

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