
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
Given three statements:
1) The equation \(x^{2} - ax + 1 = 0\) has no real roots;
2) The equality \(|a-2| = 2 - a\) holds;
3) The system of equations

\[
\begin{cases}
x + y^{2} = a \\
x - \sin^{2} y = -3
\end{cases}
\]

has a unique solution.

Find all values of \(a\) for which two of these statements are true, and one is false.

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