
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
A red long string is folded in half, and then folded in half again, ..., after being folded $m$ times, the bundle obtained is cut in the middle to get some red short strings; a white long string is folded in half, and then folded in half again, ..., after being folded $n$ times, the bundle obtained is cut in the middle to get some white short strings. If the ratio of the number of red short strings to the number of white short strings is an integer greater than 1, please give the smallest possible value of this integer.

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