
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
According to ancient traditions, the Fejszámolók tribe classifies years as either fortunate or ominous. For example, the year 2013 is considered fortunate because the first 2013 positive integers can be divided into at least two groups such that the sum of the numbers and the number of elements in each group are equal. If this is not possible, the year is classified as ominous. Which years are ominous?

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