
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
For each positive integer \( n \), let \( T(n) \) represent the number of sequences of length \( n \) composed of the letters \( A, B, \) and \( C \) with each of the following conditions:
- No more than two \( A \)'s in a row
- No more than two \( B \)'s in a row
- Exactly one \( C \) in a sequence, anywhere in the sequence.

What is the remainder when \( T(10) \) is divided by 5?
**A)** 0       
**B)** 1       
**C)** 2       
**D)** 3       
**E)** 4

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