
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 $T(n)$ is the number of sequences of length $n$ consisting solely of the letters $A$ and $B$, with no more than two $A$s in a row, no more than two $B$s in a row, and the sequence must not start with 'AA' or end with 'BB', find $T(10)$.

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