
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
Given the sum of the first K natural numbers is given by \(1 + 2 + 3 + \cdots + K = N^2\) where N^2 is a perfect square and N is less than 200, and K must be an odd number, find the possible values for K.

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