
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
Can we find 2018 distinct natural numbers, all smaller than 150,000, such that no three numbers ever form an arithmetic sequence (that is, there are never three numbers \(a, b, c\) such that \(a + c = 2b\))?

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