
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
Two moving points, $P$ and $Q$, start from point $A(1,0)$ and move along a unit circle. Point $P$ moves counterclockwise at a rate of $\dfrac{\pi}{3}$ radians per second, and point $Q$ moves clockwise at a rate of $\dfrac{\pi}{6}$ radians per second. Suppose $P$ and $Q$ meet for the first time at point $B$. The coordinates of point $B$ are \_\_\_\_\_\_.

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