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

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