
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 $2k+1$ cards, numbered with consecutive natural numbers from 1 to $2k+1$. What is the largest number of cards that can be chosen such that none of the selected numbers is equal to the sum of two other selected numbers?

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