
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
For sequence A: $a_1, a_2, \ldots, a_n$, after transformation $T$: swapping the positions of two adjacent segments in A (one item or several consecutive items in sequence A is called a segment), we get the sequence $T(A)$. For example, for sequence A: $a_1, \ldots, a_i, \overset{a_{i+1},\cdots ,a_{i+p}}{ }M, \overset{a_{i+p+1},\cdots ,a_{i+p+q}}{ }N, a_{i+p+q+1}, \ldots, a_{n}$ ($p \geq 1, q \geq 1$)  
By swapping the positions of segments M and N, the transformation results in sequence $T(A): a_1, \ldots, a_i, \overset{a_{i+p+1},\cdots ,a_{i+p+q}}{ }N, \overset{a_{i+1},\cdots ,a_{i+p}}{ }M, a_{i+p+q+1}, \ldots, a_{n}$.  
Let $A_0$ be a finite sequence, and let $A_{k+1} = T(A_k)$ ($k=0,1,2,\ldots$).  
(I) If sequence $A_0$ is 3, 2, 1, and $A_2$ is 1, 2, 3. Write out sequence $A_1$; (writing one is sufficient)  
(II) If sequence $A_0$ is 9, 8, 7, 6, 5, 4, 3, 2, 1, $A_1$ is 5, 4, 9, 8, 7, 6, 3, 2, 1, $A_2$ is 5, 6, 3, 4, 9, 8, 7, 2, 1, $A_5$ is 1, 2, 3, 4, 5, 6, 7, 8, 9. Write out sequences $A_3$, $A_4$; (writing one set is sufficient)  
(III) If sequence $A_0$ is an arithmetic sequence: 2015, 2014, …, 1, and $A_n$ is an arithmetic sequence: 1, 2, …, 2015, find the minimum value of n.

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