
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
Let  $A$  be a set of positive integers satisfying the following : $a.)$  If  $n \in A$  , then  $n \le 2018$ . $b.)$  If  $S \subset A$  such that  $|S|=3$ , then there exists  $m,n \in S$  such that  $|n-m| \ge \sqrt{n}+\sqrt{m}$ What is the maximum cardinality of  $A$  ?

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