
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 equally spaced and numbered sequentially from 1 to 100. Simultaneously, Petya and Vasya start walking towards each other from opposite ends of the alley at different constant speeds (Petya from the first lamppost and Vasya from the hundredth lamppost). When Petya is at 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 lamppost number in the answer.

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