
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
Let $S_n$ denote the sum of the first $n$ terms of an arithmetic sequence with common difference 5. If $\frac{S_{4n}}{S_n}$ is a constant that does not depend on $n$ for all positive integers $n$, find the first term of the sequence.

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