
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
Consider a unique strictly increasing sequence of nonnegative integers \( b_1, b_2, \ldots, b_m \) where \(b_1 < b_2 < \ldots < b_m\) such that
\[
\frac{2^{171} + 1}{2^{19} + 1} = 2^{b_1} + 2^{b_2} + \ldots + 2^{b_m}.
\]
Determine the value of \( m \).
A) 97
B) 100
C) 101
D) 105
E) 110

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