
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
Define the sequence \((y_n)\) by letting \(y_1 = 128\) and \(y_k = y_{k-1}^2 - y_{k-1}\) for all \(k \geq 2\). Compute the sum:
\[
\frac{1}{y_1 - 1} + \frac{1}{y_2 - 1} + \frac{1}{y_3 - 1} + \dotsb.
\]

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