
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
Call an integer  $k$  *debatable* if the number of odd factors of  $k$  is a power of two. What is the largest positive integer  $n$  such that there exists  $n$  consecutive debatable numbers? (Here, a power of two is defined to be any number of the form  $2^m$ , where  $m$  is a nonnegative integer.)

*Proposed by Lewis Chen*

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