
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 \( x_1x_2 + x_2x_3 + \cdots + x_5x_1 \) where \( x_1, x_2, \dots, x_5 \) is a permutation of \( (1,2,3,4,6) \). 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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