
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 a permutation  $\pi$  of the integers from 1 to 10, define
\[ S(\pi) = \sum_{i=1}^{9} (\pi(i) - \pi(i+1))\cdot (4 + \pi(i) + \pi(i+1)), \]
where  $\pi (i)$  denotes the  $i$ th element of the permutation. Suppose that  $M$  is the maximum possible value of  $S(\pi)$  over all permutations  $\pi$  of the integers from 1 to 10. Determine the number of permutations  $\pi$  for which  $S(\pi) = M$ .

*Ray Li*

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