
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
To determine the parameters \( a_{1}, a_{2}, \) and \( a_{3} \) in the formula \( y=a_{1} x^{2}+a_{2} x+a_{3} \), values of \( y \) were measured at various values of \( x \). The sample obtained is:

\[
\begin{array}{rrrrrrrrrr}
x_{k} & -1 & -0.75 & -0.5 & -0.25 & 0 & 0.25 & 0.5 & 0.75 & 1 \\
y_{k} & 6.01 & 5.07 & 4.30 & 3.56 & 3.07 & 2.87 & 2.18 & 2.00 & 2.14
\end{array}
\]

Using these data, determine the parameters \( a_{1}, a_{2} \), and \( a_{3} \) by the method of least squares. Measurement errors of \( x_{1}, \ldots, x_{9} \) and computational inaccuracies can be neglected.

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