
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 $t_k$ be the sum of the $k$th powers of the roots of the polynomial $x^3 - 6x^2 + 11x - 6$. If $t_0 = 3$, $t_1 = 6$, and $t_2 = 14$, determine the constants $a$, $b$, and $c$ such that $t_{k+1} = a t_k + b t_{k-1} + c t_{k-2}$ for $k = 2$, $3$, $...$. What is $a+b+c$?
A) 3 
B) 4 
C) 5 
D) 6 
E) 7

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