
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 \( x = -\sqrt{2} + \sqrt{3} + \sqrt{5} \), \( y = \sqrt{2} - \sqrt{3} + \sqrt{5} \), and \( z = \sqrt{2} + \sqrt{3} - \sqrt{5} \). What is the value of the expression below?
$$
\frac{x^{4}}{(x-y)(x-z)} + \frac{y^{4}}{(y-z)(y-x)} + \frac{z^{4}}{(z-x)(z-y)}
$$

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