
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 $2+\frac{2}{3}={2}^{2}\times \frac{2}{3}$, $3+\frac{3}{8}={3}^{2}\times \frac{3}{8}$, $4+\frac{4}{15}={4}^{2}\times \frac{4}{15}$, determine the value of $a+b$, where $a$ and $b$ are positive integers in the equation $9+\frac{b}{a}={9}^{2}\times \frac{b}{a}$.

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