
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
The number of students who won the first prize in the senior high school math competition is between 30 and 55. During the award ceremony, photos were taken of the students who won the first prize. When arranged in 3 columns, there are 2 extra students; when arranged in 5 columns, there are 4 extra students; when arranged in 7 columns, there are 2 extra students. How many students won the first prize?

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