
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
Given that \(a, b, c,\) and \(d\) are all integers, and \(m = a^2 + b^2\) and \(n = c^2 + d^2\), express \(mn\) as a sum of squares of two integers. The form is: \(mn =\) \[\_\_\_\]

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