
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 \(1 + 2 + 3 + \cdots + K\) equals \(M^2\) for some integer \(M\) and if \(M\) is less than \(200\) and \(K\) is greater than \(M\), determine the possible values of \(K\).
**A)** Only 8  
**B)** Only 49  
**C)** Both 8 and 49  
**D)** 1 and 8  
**E)** 1, 8, and 49

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