
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
Find the largest possible value of \(y\) in the simplified form \(y = \frac{p + q\sqrt{r}}{s}\) if \(\frac{7y}{8} + 2 = \frac{4}{y}\), where \(p, q, r,\) and \(s\) are integers. What is \(\frac{prs}{q}\)?

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