
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, there are 100 lampposts placed at equal intervals, numbered sequentially from 1 to 100. At the same moment, Petya and Vasya start walking towards each other from opposite ends of the alley at different constant speeds (Petya starts at the first lamppost and Vasya starts at the hundredth lamppost). When Petya reaches the 22nd lamppost, Vasya is at the 88th lamppost. At which lamppost will they meet? If the meeting occurs between two lampposts, indicate the smaller of the two lamppost numbers in the answer.

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