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

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