
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
Let \(a, b, c, d\) be real numbers such that

\[
\left\{
\begin{array}{l}
a^2 + b^2 + 2a - 4b + 4 = 0 \\
c^2 + d^2 - 4c + 4d + 4 = 0
\end{array}
\right.
\]

Let \(m\) and \(M\) be the minimum and the maximum values of \((a-c)^2 + (b-d)^2\), respectively. What is \(m \times M\)?

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