
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 the unique strictly increasing sequence of nonnegative integers $a_1 < a_2 < \ldots < a_m$ such that
\[
\frac{2^{300} + 1}{2^{20} + 1} = 2^{a_1} + 2^{a_2} + \ldots + 2^{a_m}.
\]
Determine the value of $m$.
A) 135
B) 140
C) 145
D) 150
E) 155

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