
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
When \(\left(a_{1}, a_{2}, \cdots, a_{n}\right)\) takes all permutations of \((1, 2, \cdots, n)\), find the average value of the expression
$$
\left(a_{1} - a_{2}\right)^{2} + \left(a_{2} - a_{3}\right)^{2} + \cdots + \left(a_{n-1} - a_{n}\right)^{2}.
$$

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