
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 friends left school No. 15 after the olympiad and went in opposite directions, pondering a difficult problem. Misha walked 8 km per hour, while Vasya walked half that distance in an hour. 45 minutes later, they found a solution to the problem and ran toward each other to share their solution, each increasing their speed by one and a half times. How much time did it take for them to meet? What distance did they cover before meeting?

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