
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 vector $\overrightarrow{OA} = (1, 1)$, it is rotated counterclockwise around the origin $O$ by $60^{\circ}$ to obtain $\overrightarrow{OB}$. Determine the coordinates of $\overrightarrow{OB}$.

A) $(\frac{1 - \sqrt{3}}{2}, \frac{1 + \sqrt{3}}{2})$
B) $(\frac{1 + \sqrt{3}}{2}, \frac{1 - \sqrt{3}}{2})$
C) $(\frac{-1 - \sqrt{3}}{2}, \frac{-1 + \sqrt{3}}{2})$
D) $(\frac{-1 + \sqrt{3}}{2}, \frac{-1 - \sqrt{3}}{2})$

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