
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
A subset of  $X$  of  $\{1,2,3, \ldots 10000 \}$  has the following property: If  $a,b$  are distinct elements of  $X$ , then  $ab\not\in X$ . What is the maximal number of elements in  $X$ ?

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