
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
Shan solves the simultaneous equations
$$
xy = 15 \text { and } (2x - y)^4 = 1
$$
where \(x\) and \(y\) are real numbers. She calculates \(z\), the sum of the squares of all the \(y\)-values in her solutions. What is the value of \(z\)?

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