
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
There are 100 street lamps positioned at equal intervals along a straight alley, numbered consecutively from 1 to 100. Petya and Vasya start walking towards each other at different constant speeds from opposite ends of the alley (Petya starts from lamp 1, Vasya from lamp 100). When Petya is at lamp 22, Vasya is at lamp 88. At which lamp will they meet? If the meeting happens between two lamps, specify the lower-numbered lamp in your answer.

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