
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
A certain abrasive tool factory has six production workshops. The first, second, third, and fourth workshops produce the same number of products each day. The fifth and sixth workshops produce $\frac{3}{4}$ and $\frac{8}{3}$ times the number of products produced by the first workshop each day, respectively. Inspectors A and B are stationed in the factory to inspect the products. When they start inspecting the products simultaneously, each workshop has the same number of finished products. During the inspection period, the workshops continue production. Inspector A takes 6 days to inspect all the products from the first, second, and third workshops simultaneously. Inspector B first takes 2 days to inspect all the products from the fourth and fifth workshops simultaneously, and then takes 4 more days to inspect all the products from the sixth workshop (including the original products and those produced during the inspection period). If the inspection speed of each inspector is the same, then the ratio of the number of inspectors in group A to group B is ____.

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