
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
Matvey left Totma, and at the same time, Peter ran to meet him from Kaluga on the same road. Under identical conditions, the boys' speeds are in a ratio of $2:3$ and are constant. At some point on their way, they encounter rough terrain (possibly at different times) which continues until they meet. On the rough terrain, each person's speed drops to half. How do the distances traveled on rough terrain by Peter and Matvey compare if they meet exactly halfway between the cities and the rough terrain makes up $2/3$ of the distance between Kaluga and Totma?

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