
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 groups set out on a walking tour: one departs from Budapest heading towards Hatvan at a speed of $8 \mathrm{~km} / \mathrm{h}$, while the other departs from Hatvan heading towards Budapest at a speed of $6 \mathrm{~km} / \mathrm{h}$. When will they meet if they set out at the same time and follow the same route? Every hour, the first group's speed decreases by $1 \mathrm{~km} / \mathrm{h}$, and the second group's speed decreases by $0.5 \mathrm{~km} / \mathrm{h}$. (Assume the distance between Hatvan and Budapest is $60 \text{ km}$.)

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