
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 runners, $\alpha$ and $\β$, are racing on a circular track. The distance is one lap, with the start and finish at point $P$. When $\alpha$ reaches point $Q$, which is halfway around the track, $\beta$ is $16 \mathrm{~m}$ behind. At a later time, the two runners' positions are symmetric with respect to the diameter $PQ$. $1 \frac{2}{15}$ seconds after this moment, $\beta$ reaches point $Q$, and $13 \frac{13}{15}$ seconds later, $\alpha$ finishes the race. What are the speeds of the runners and what is the distance of the lap? (Assume both runners maintain a constant speed.)

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