
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 that the sum $1 + 2 + 3 + \cdots + K$ equals a perfect square $N^2$, and that $N$ is less than $50$, determine the possible values for $K$.
A) Only 1  
B) 1 and 8  
C) Only 8  
D) 8 and 49  
E) 1, 8, and 49

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