
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
Solve for the maximum possible value of $x$ in the form $x = \frac{p+q\sqrt{r}}{s}$ when $\frac{7x}{5} + 2 = \frac{4}{x}$, where $p, q, r$, and $s$ are integers. What is $\frac{prs}{q}$?

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