
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
Determine the number of ways to select a sequence of  $ 8$  sets  $ A_1,A_2,\ldots,A_8$ , such that each is a subset (possibly empty) of  $ \{1,2\}$  and  $ A_m$  contains  $ A_n$  if  $ m$  divides  $ n$ .

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