
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
Given that for each positive integer $n$, let $S(n)$ be the number of sequences of length $n$ consisting solely of the letters A and B, with no more than three A's in a row and no more than three B's in a row, find the remainder when $S(2015)$ is divided by $12$.

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