
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
Find all subsets  $A$  of  $\left\{ 1, 2, 3, 4, \ldots \right\}$ , with  $|A| \geq 2$ , such that for all  $x,y \in A, \, x \neq y$ , we have that  $\frac{x+y}{\gcd (x,y)}\in A$ .

*Dan Schwarz*

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