
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 the values of the parameter \( a \) for which the system

\[ 
\begin{cases}
y = |x - \sqrt{a}| + \sqrt{a} - 2 \\
(|x| - 4)^{2} + (|y| - 3)^{2} = 25
\end{cases}
\]

has exactly three solutions.

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