
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 \( T(n) \) be the number of sequences of length \( n \) consisting solely of the letters \( A \), \( B \), and \( C \), with no more than two \( A \)s in a row, no more than two \( B \)s in a row, and no more than one \( C \) in a row. Moreover, sequences cannot end with the letter \( C \). What is the remainder when \( T(10) \) is divided by \( 5 \)?
A) 1
B) 2
C) 3
D) 4
E) 0

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