
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
Point $A$ and $B$ move counterclockwise on circle $\odot O$ with center at the origin $O$ and radius $1$, starting at the same time. The angular velocity of $A$ is $3$ rad/s, starting at the intersection of circle $\odot O$ and the positive $x$-axis; the angular velocity of $B$ is $1$ rad/s, starting at the intersection of the line $y=\sqrt{3}x$ ($x\geqslant 0$) and circle $\odot O$. When $A$ and $B$ coincide, determine the coordinates of point $A$.

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