
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
Given a string of length  $2n$ , we perform the following operation:

        
- Place all the even indexed positions together, and then all the odd indexed positions next. Indexing is done starting from  $0$ .[/*]

    For example, say our string is ``abcdef''. Performing our operation yields ``abcdef''  $\to$  ``acebdf''. Performing the operation again yields ``acebdf''  $\to$  ``aedcbf''. Doing this repeatedly, we have:
    ``abcdef''  $\to$  ``acebdf''  $\to$  ``aedcbf''  $\to$  ``adbecf''  $\to$  ``abcdef''.
    You can assume that the characters in the string will be unique. It can be shown that, by performing the above operation a finite number of times we can get back our original string.
    Given  $n$ , you have to determine the minimum number of times the operation must be performed to get our original string of length  $2n$  back.
    In the example given above,  $2n = 6$ . The minimum steps required is  $4$ .

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