
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
Along a straight alley, 100 lanterns are placed at equal intervals, numbered sequentially from 1 to 100. Simultaneously, Petya and Vasya start walking towards each other from opposite ends of the alley with different constant speeds (Petya starts from the first lantern, and Vasya starts from the hundredth lantern). When Petya reached the 22nd lantern, Vasya was at the 88th lantern. At which lantern will they meet? If the meeting occurs between two lanterns, indicate the smaller number of the two.

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