
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 positive numbers \(A\), \(B\), \(C\), and \(D\) are such that the system of equations

\[ x^{2}+y^{2}=A \]
\[ |x|+|y|=B \]

has \(m\) solutions, and the system of equations

\[ x^{2}+y^{2}+z^{2}=C \]
\[ |x|+|y|+|z|=D \]

has \(n\) solutions. It is known that \(m > n > 1\). Find \(m\) and \(n\).

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