
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
Calculate how many terms $k$ there are in the strictly increasing sequence of nonnegative integers $b_1 < b_2 < \ldots < b_k$ such that:
\[
\frac{2^{255} + 1}{2^{15} + 1} = 2^{b_1} + 2^{b_2} + \ldots + 2^{b_k}
\]
A) 120
B) 128
C) 136
D) 144

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