
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 person has a cabinet where he stores a collection of bird eggs. This cabinet has 12 drawers, and all of them (except the top one, which holds a catalog) are divided into compartments by wooden dividers, each of which extends the full length or width of the corresponding drawer. In each successive drawer, the number of compartments is greater than in the previous one. The bottom drawer (No. 12) has compartments 12 times the number of dividers, drawer number 11 has compartments 11 times the number of dividers, and so on.

How are the drawers divided (how many compartments and dividers are there in each drawer)? In each case, specify the minimum possible number of compartments and dividers.

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