
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 all sets of real numbers  $S$  such that:



- $1$  is the smallest element of  $S$ ,
- for all  $x,y\in S$  such that  $x>y$ ,  $\sqrt{x^2-y^2}\in S$


*Adian Anibal Santos Sepcic*

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