
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 system of two second-degree equations

$$
\left\{
\begin{array}{r}
x^{2} - y^{2}=0 \\
(x-a)^{2} + y^{2} = 1 
\end{array}
\right.
$$

generally has four solutions. For which values of \(a\) does the number of solutions decrease to three or two?

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