
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
The sequence $(y_n)$ is defined by $y_1 = 150$ 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