
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
The numbers $n, n+1, \ldots, N$ need to be divided into two classes such that neither class contains three different numbers, $x, y, z$, for which $x+y=z$. What is the maximum value of $N$ for which this condition can be satisfied?

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