
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 $\sqrt{2+ \frac{2}{3}} =2\sqrt{\frac{2}{3}}$, $\sqrt{3+ \frac{3}{8}} =3\sqrt{\frac{3}{8}}$, $\sqrt{4+ \frac{4}{15}} =4\sqrt{\frac{4}{15}}$, ..., if $\sqrt{6+ \frac{a}{t}} =6\sqrt{\frac{a}{t}}$ (where $a,t$ are positive real numbers), then by analogy with the above equations, we can infer the values of $a$ and $t$, $a+t=$ ______.

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