
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 \( x \) in the simplified form \( x = \frac{a + b\sqrt{c}}{d} \) if \( \frac{7x}{9} + 2 = \frac{4}{x} \), where \( a, b, c, \) and \( d \) are integers. What is \( \frac{acd}{b} \)?

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