
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
Péter sent his son with a message to his brother, Károly, who in turn sent his son to Péter with a message. The cousins met $720 \, \text{m}$ away from Péter's house, had a 2-minute conversation, and then continued on their way. Both boys spent 10 minutes at the respective relative's house. On their way back, they met again $400 \, \text{m}$ away from Károly's house. How far apart do the two families live? What assumptions can we make to answer this question?

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