
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 a common difference of 5. If the ratio \( \frac{S_{4n}}{S_n} \) 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