
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 $2+ \frac{2}{3}=2^{2} \times \frac{2}{3}$, $3+ \frac{3}{8}=3^{2} \times \frac{3}{8}$, $4+ \frac{4}{15}=4^{2} \times \frac{4}{15}$, ..., if $9+ \frac{b}{a}=9^{2} \times \frac{b}{a}$ ($a,b$ are positive integers), then $a+b=$ ___.__

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