
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
We use \( S_{k} \) to represent an arithmetic sequence with the first term \( k \) and common difference \( k^{2} \). For example, \( S_{3} \) is \( 3, 12, 21, \cdots \). If 306 is a term in \( S_{k} \), the sum of all possible \( k \) that satisfy this condition is ____.

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