
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 the equations $\sqrt{2+\frac{2}{3}}=2\sqrt{\frac{2}{3}}$, $\sqrt{3+\frac{3}{8}}=3\sqrt{\frac{3}{8}}$, and $\sqrt{4+\frac{4}{15}}=4\sqrt{\frac{4}{15}}$, if $\sqrt{6+\frac{a}{b}}=6\sqrt{\frac{a}{b}}$, where $a$ and $b$ are real numbers, guess the values of $a$ and $b$.

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