
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 \( A \) be a finite set such that
\[
\begin{array}{l}
|A| \geqslant 2, \\
Q(A) = \left\{ \left. \frac{a - b}{c - d} \right| a, b, c, d \in A, c \neq d \right\}.
\end{array}
\]
Find the smallest real number \( \lambda \) such that \( |Q(A)| \leqslant \lambda |A|^4 \) holds for all sets \( A \).

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