
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
There is a sequence of numbers  $+1$  and  $-1$  of length  $n$ . It is known that the sum of every  $10$  neighbouring numbers in the sequence is  $0$  and that the sum of every  $12$  neighbouring numbers in the sequence is not zero. What is the maximal value of  $n$ ?

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