
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 travel toward each other from points \(A\) and \(B\) with speeds \(v_{1} = 6 \, \mathrm{m/s}\) and \(v_{2} = 4 \, \mathrm{m/s}\). At the moment they meet, one of them turns around and walks in the opposite direction, while the other does not change direction. The person who did not change direction reached their final destination \(t_{2} = 10\) minutes earlier than the person who turned around. Determine the time \(t_{1}\) that passed from the start of the journey until the meeting. (15 points)

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