
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 a geometric sequence with \(n\) terms, where the first term is 1, the common ratio is \(r\), and the sum is \(s\), all of which are non-zero, find the sum of the new geometric sequence after each term of the original sequence is replaced with its reciprocal.

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