
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 set  $S$  of natural numbers is called *good*, if for each element  $x \in  S, x$  does not divide the sum of the remaining numbers in  $S$ . Find the maximal possible number of elements of a *good*set which is a subset of the set  $A = \{1,2, 3,  ...,63\}$ .

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