
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 \( x, y, z, u \in \mathbf{Z} \) with \( 1 \leqslant x, y, z, u \leqslant 10 \), find the number of ordered quadruples \((x, y, z, u)\) that satisfy the inequality:
\[ \frac{x-y}{x+y}+\frac{y-z}{y+z}+\frac{z-u}{z+u}+\frac{u-x}{u+x} > 0 \]

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