
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
There exists a unique strictly increasing sequence of nonnegative integers \(b_1 < b_2 < ... < b_s\) such that
\[
\frac{2^{305}+1}{2^{17}+1} = 2^{b_1} + 2^{b_2} + ... + 2^{b_s}.
\]
Determine the smallest \(s\) for which \( \frac{2^{305}+1}{2^{17}+1} \leq 2^{b_1} + 2^{b_2} + ... + 2^{b_s}.\)
A) 137
B) 285
C) 289
D) 294
E) 306

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