
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 $x+\frac{1}{x}=a$ has no real solutions;
2) The equality $\sqrt{a^{2}-4 a+4}=2-a$ holds;
3) The system $\left\{\begin{array}{l}x+y^{2}=a, \\ x-\sin ^{2} y=-3\end{array}\right.$ has a unique solution.

For which values of $a$ will two of these statements be true, and the third one false?

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