
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
The Fibonacci numbers are defined by  $F_1=F_2=1$  and  $F_n=F_{n-1}+F_{n-2}$  for  $n>2$ .  It is well-known that the sum of any  $10$  consecutive Fibonacci numbers is divisible by  $11$ .  Determine the smallest integer  $N$  so that the sum of any  $N$  consecutive Fibonacci numbers is divisible by  $12$ .

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