
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 an odd positive integer $n$, the sequence $\{a_n\}$: $a_1, a_2, \ldots, a_n$ is a permutation of $1, 2, \ldots, n$. Define $E(a_1, a_2, \ldots, a_n) = |a_1-1| + |a_2-2| + \ldots + |a_n-n|$ as the sum of position differences for the sequence $\{a_n\}$: $a_1, a_2, \ldots, a_n$.
- (I) When $n=5$, the sum of position differences for the sequence $\{a_n\}$: $1, 3, 4, 2, 5$ is \_\_\_\_\_\_.
- (II) If the sum of position differences $E(a_1, a_2, \ldots, a_n) = 4$, the number of sequences $\{a_n\}$: $a_1, a_2, \ldots, a_n$ that satisfy this condition is \_\_\_\_\_\_ (expressed in terms of $n$).

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