
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 $a,$ $b,$ $c$ be the roots of $x^3 - rx^2 + sx - t = 0.$ Express
\[
\begin{vmatrix} 
2 + a & 2 & 2 \\ 
2 & 2 + b & 2 \\
2 & 2 & 2 + c 
\end{vmatrix}
\]
in terms of $r$, $s$, and $t$.

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