
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
On a real number line, the points  $1, 2, 3, \dots, 11$  are marked. A grasshopper starts at point  $1$ , then jumps to each of the other  $10$  marked points in some order so that no point is visited twice, before returning to point  $1$ . The maximal length that he could have jumped in total is  $L$ , and there are  $N$  possible ways to achieve this maximum. Compute  $L+N$ .

*Proposed by Yannick Yao*

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