
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
A certain type of signal dampens over time, where the strength at each successive second is a fixed fraction of its strength a second before. The signal starts with a strength \( s \) and the dampening factor is \( r \) (including the sign). The series representing total signal strength over an infinite time \( s + sr + sr^2 + \cdots \) has a total of \( 16 \) units. The strength of the signals occurring at odd seconds, modeled by \( sr + sr^3 + sr^5 + \cdots \), sums up to \( -6 \) units, since these signals are weaker due to interference. Calculate the dampening factor \( r \).

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