
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
Given that \( x \) and \( y \) are positive numbers with \( xy = \frac{1}{9} \), \( x(y+1) = \frac{7}{9} \), and \( y(x+1) = \frac{5}{18} \), calculate the value of \( (x+1)(y+1) \).

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