
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  $S$  of the set of integers 0 - 99 is said to have property  $A$  if it is impossible to fill a crossword-puzzle with 2 rows and 2 columns with numbers in  $S$  (0 is written as 00, 1 as 01, and so on). Determine the maximal number of elements in the set  $S$  with the property  $A.$ 

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