
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 set of positive integers  $X$  is called *connected* if  $|X|\ge 2$  and there exist two distinct elements  $m$  and  $n$  of  $X$  such that  $m$  is a divisor of  $n$ .
Determine the number of connected subsets of the set  $\{1,2,\ldots,10\}$ .

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