
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
Let $M$ be the maximum possible value of $x_1x_2+x_2x_3+\dots+x_6x_1$ where $x_1, x_2, \dots, x_6$ is a permutation of $(2,3,4,5,6)$, and let $N$ be the number of permutations for which this maximum is attained. Evaluate $M+N$.

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