
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
If the sum $1 + 3 + 5 + \cdots + K$ is a perfect square $N^2$ and $K$ is an odd number with $N$ less than $50$, then the possible values for $K$ are:
**A)** only $1$  
**B)** $1, 3, 9$  
**C)** $1, 3, 5, 7, \dots, 97$  
**D)** $1, 3, 5, 9, 49$  
**E)** $1, 3, 5, 9, 15$

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