
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 street lamps placed at equal intervals, numbered from 1 to 100 in order. Simultaneously, Petya and Vasya start walking towards each other from opposite ends of the alley at different constant speeds (Petya from the first lamp, Vasya from the hundredth lamp). When Petya is at the 22nd lamp, Vasya is at the 88th lamp. At which lamp will they meet? If the meeting occurs between two lamps, provide the smaller number of the two.

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