
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
The distance between Moscow and Smolensk by rail is 415 km. On this route, the cities of Mozhaysk and Vyazma are located. The distance between Moscow and Mozhaysk is in the ratio of $7:9$ to the distance between Mozhaysk and Vyazma, and the distance between Mozhaysk and Vyazma is $27/35$ of the distance between Vyazma and Smolensk. Find the distances between each pair of neighboring cities.

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