
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
Given the set $S=\{(x,y)|1\leqslant x\leqslant 10,1\leqslant y\leqslant 10,x\in \mathbb{N},y\in \mathbb{N}\}$. If $A\subseteq S$, and for any $(a,b)\in A$, $(s,t)\in A$, we have $(a-s)(b-t)\leqslant 0$, calculate the maximum number of elements in set $A$.

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