
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
Two factories, A and B, collaborated to produce a batch of protective clothing. They started work at the same time. Initially, factory A's production speed was $\frac{1}{3}$ faster than factory B's. Midway, factory B stopped for 1 day to adjust its machinery, after which its production speed doubled. It took a total of 6 days from start to finish, and both factories produced the same amount of protective clothing. How many days did the two factories work after factory B adjusted its machinery?

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