
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 \( y_1 = 200 \) and \( y_k = y_{k - 1}^2 - y_{k - 1} \) for all \( k \ge 2 \). Compute
\[
\frac{1}{y_1 + 1} + \frac{1}{y_2 + 1} + \frac{1}{y_3 + 1} + \dotsb.
\]

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