
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  $g(n)$  be the number of all  $n$ -digit natural numbers each consisting only of digits  $0,1,2,3$  (but not nessesarily all of them) such that the sum of no two neighbouring digits equals  $2$ . Determine whether  $g(2010)$  and  $g(2011)$  are divisible by  $11$ .

I.Kozlov

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