
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
Workshops A and B both produce the same type of component. In workshop A, there is 1 person who produces 6 components per day, and the rest produce 11 components per day. In workshop B, there is 1 person who produces 7 components per day, and the rest produce 10 components per day. It is known that the total number of components produced by each workshop is equal, and the total is not less than 100 and not more than 200. How many people are there in workshops A and B, respectively?

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