
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
Five students from different cities of the region came to Kirov to participate in the regional math Olympiad. Each was asked which city they came from. The first student said, "I came from Yaransk, and the fourth among us is from Lalsk." The second said, "I came from Yaransk, and the third from Khalturin." The third said, "I came from Yaransk, and the fourth from Slobodskoy." The fourth said, "I came from Lalsk, and the fifth from Kotel'nich." Finally, the fifth said that he really came from Kotel'nich, and the first from Slobodskoy. It was determined that of the two statements made by each student, one is true and the other is false. From which city did each student come?

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