
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
Find all values of parameter \( a \) for which the system of equations
\[ \left\{ \begin{array}{c} 4 \sqrt{y} = x - a, \\ y^{2} - x^{2} + 2 y - 4 x - 3 = 0 \end{array} \right. \]
has a unique solution. Indicate this solution for each \( a \).

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