
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 people are moving towards each other from points \( A \) and \( B \) with speeds \( v_{1}=6 \, \text{m/s} \) and \( v_{2}=4 \, \text{m/s} \). At the moment they meet, one of them turns around and goes in the opposite direction, while the other does not change their direction of movement. The person who turned around, upon returning to the starting point of their journey, waits for the other person and waits for \( t_{2}=10 \, \text{minutes} \). Determine how much time \( t_{1} \) passed from the beginning of the journey until the moment they met. (15 points)

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