
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 smallest possible value of \(x\) in the simplified form \(x=\frac{a+b\sqrt{c}}{d}\) if \(\frac{7x}{8}-1=\frac{4}{x}\), where \(a, b, c,\) and \(d\) are integers. What is \(\frac{acd}{b}\)?

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