
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 \(x=\frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}}\), \(y=\frac{\sqrt{7}-\sqrt{3}}{\sqrt{7}+\sqrt{3}}\) and \(192 z=x^{4}+y^{4}+(x+y)^{4}\). Find the value of \(z\).

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