
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
The discriminant \( D = (1-\xi)^{2} + 4 \xi(\xi+2) = 0 \rightarrow 5 \xi^{2} + 6 \xi + 1 = 0 \rightarrow 
\begin{array}{c}
\xi = -1 \\
\xi = -1/5 
\end{array} \)

The probability that \(\xi\) takes on one of the values \(-1\) or \(-1/5\) is \( P(A) = \frac{3}{16} + \frac{1}{4} = \frac{7}{16} \).

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