
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
A tourist and a cyclist simultaneously set out from point $A$ to point $B$, which are 8 km apart. After spending no less than half an hour on the way from $A$ to $B$, the cyclist, without stopping, turned back and started moving towards point $A$, increasing his speed by $25\%$. Ten minutes after his departure from point $B$, the cyclist met the tourist. Determine the greatest possible whole value of the tourist's speed (in km/h), and for this speed, find the cyclist's original speed.

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