
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
For which values of the parameter \(a\) does the system of equations

$$
\left\{\begin{array}{c}
\frac{\left(y^{2}-2 x y-y+8 x-12\right) \sqrt{x+1}}{\sqrt{4-x}} \\
2x + y - a = 0
\end{array}\right. = 0
$$

have two solutions?

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