
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
Several people were collecting mushrooms. One found 6 mushrooms, and each of the others found 13. Another time, the number of collectors was different. This time, one found 5 mushrooms, and each of the others found 10. In both cases, the same number of mushrooms was collected, more than 100 but less than 200. Find the number of mushroom collectors in each case.

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