
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
There are  $100$  cards with numbers from  $1$  to  $100$  on the table.Andriy and Nick took the same number of cards in a way such that the following condition holds:if Andriy has a card with a number  $n$  then Nick has a card with a number  $2n+2$ .What is the maximal number of cards that could be taken by the two guys?

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