
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
Consider the set  $X$  =  $\{ 1,2 \ldots 10 \}$  . Find two disjoint nonempty sunsets  $A$  and  $B$  of  $X$  such that 

a)  $A \cup B = X$ ;

b)  $\prod_{x\in A}x$  is divisible by  $\prod_{x\in B}x$ , where  $\prod_{x\in C}x$  is the product of all numbers in  $C$ ;

c)  $\frac{ \prod\limits_{x\in A}x}{ \prod\limits_{x\in B}x}$   is as small as possible.

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