
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 $t_k$ denote the sum of the $k$th powers of the roots of the polynomial $x^3 - 6x^2 + 11x - 6$. The polynomial's roots enable the determination of $t_0=3$, $t_1=6$, and $t_2=14$. Let $d$, $e$, and $f$ be constants such that $t_{k+1} = d \, t_k + e \, t_{k-1} + f \, t_{k-2}$ for $k = 2$, $3$, $...$. What is $d+e+f$?
A) 10
B) 11
C) 12
D) 13
E) 14

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