
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 the parameter \( a \) for which the system

\[ \left\{\begin{array}{l} 
|y-3-x| + |y-3+x| = 6 \\ 
(|x| - 4)^{2} + (|y| - 3)^{2} = a 
\end{array}\right. \]

has exactly two solutions.

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