
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
Real numbers \( x_{1}, x_{2}, x_{3}, x_{4} \in [0,1] \). Find \( K_{\max} \), where
$$
\begin{aligned}
K= & \left|x_{1}-x_{2}\right|\left|x_{1}-x_{3}\right|\left|x_{1}-x_{4}\right|\left|x_{2}-x_{3}\right| \cdot \\
& \left|x_{2}-x_{4}\right|\left|x_{3}-x_{4}\right|.
\end{aligned}
$$

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