
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
The spikiness of a sequence \(a_{1}, a_{2}, \ldots, a_{n}\) of at least two real numbers is the sum \(\sum_{i=1}^{n-1}\left|a_{i+1}-a_{i}\right|\). Suppose \(x_{1}, x_{2}, \ldots, x_{9}\) are chosen uniformly and randomly from the interval \([0,1]\). Let \(M\) be the largest possible value of the spikiness of a permutation of \(x_{1}, x_{2}, \ldots, x_{9}\). Compute the expected value of \(M\).

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