
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: 
$$
\sqrt{2 + \frac{2}{3}} = 2\sqrt{\frac{2}{3}}, \quad 
\sqrt{3 + \frac{3}{8}} = 3\sqrt{\frac{3}{8}}, \quad
\sqrt{4 + \frac{4}{15}} = 4\sqrt{\frac{4}{15}}, \ldots
$$
suppose we have 
$$
\sqrt{n + \frac{a}{t}} = n\sqrt{\frac{a}{t}}
$$
where $a$, $t$, and $n$ are positive real numbers with $n \geq 2$. Through inductive reasoning, we want to conjecture the values of $a$ and $t$. Find $a + t$ in terms of $n$.

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