
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 geometric meaning of complex number multiplication $(x+yi)(\cos\theta+i\sin\theta)$ (where $x, y \in \mathbb{R}$, and $i$ is the imaginary unit) is to rotate the point corresponding to the complex number $x+yi$ in the complex plane around the origin in the counterclockwise direction by an angle $\theta$, find the coordinates of the point obtained by rotating the point $(6, 4)$ around the origin in the counterclockwise direction by $\frac{\pi}{3}$.

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