
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
Let $I_{n}$ be the set of the first $n$ odd natural numbers. For example: $I_{3}=\{1,3,5\}, I_{6}=\{1,3,5,7,9,11\}$, etc.

For which numbers $n$ can the set $I_{n}$ be divided into two (disjoint) parts such that the sums of the numbers in each part are equal?

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