
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
After the implementation of the "double reduction" policy in the country, students' extracurricular activities have become more diverse. In preparation for the New Year's activities, the art interest group of Class 7-1 needs to complete the paper-cutting task assigned by the school. If each person cuts $10$ pieces, there will be $6$ pieces of colored paper left uncut; if each person cuts $12$ pieces, there will be a shortage of $6$ pieces of colored paper. How many students are there in this group?

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