
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 $\sqrt{2 + \frac{2}{3}} = 2\sqrt{\frac{2}{3}}$, $\sqrt{3 + \frac{3}{8}} = 3\sqrt{\frac{3}{8}}$, $\sqrt{4 + \frac{4}{15}} = 4\sqrt{\frac{4}{15}}$, ..., $\sqrt{6 + \frac{a}{b}} = 6\sqrt{\frac{a}{b}}$ (where $a,b$ are real numbers), please infer the values of $a=$ _______ and $b=$ _______.

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