
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
 $ S\subset\mathbb N$  is called a square set, iff for each  $ x,y\in S$ ,  $ xy\plus{}1$  is square of an integer.
a) Is  $ S$  finite?
b) Find maximum number of elements of  $ S$ .

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