
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 $\mathcal{T}_{n}$ be the set of strings of length $n$ consisting only of the characters 'A', 'B', and 'C' such that no three consecutive characters are all the same. For example, 'AABCB' works, but 'AAABB' does not. Find the number of elements in $\mathcal{T}_{8}$.

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