
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 points move on the $y$-axis, and their positions at time $t$ are determined by the functions $y_{1}=({t-\frac{π}{3}})\sin t$ and $y_{2}=\frac{1}{2}-\cos t$. Find the moments $t$ when the two points coincide within the time interval $\left(0,2\pi \right)$.

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