
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
Let's call the "complexity" of a given number the shortest length of a numerical sequence (if such exists) that starts with zero and ends with this number, where each subsequent member of the sequence is either half of the previous one or sums with the previous one to equal 1. Among all numbers of the form \( m / 2^{50} \), where \( m=1,3,5, \ldots, 2^{50}-1 \), find the number with the greatest "complexity".

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