
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
The graph of the function $y = a^{x+3} - 2$ (where $a > 0$ and $a \neq 1$) always passes through a fixed point A, and point A lies on the line $mx + ny + 1 = 0$ (where $m > 0$, $n > 0$). Find the minimum value of $\frac{1}{m} + \frac{3}{n}$.

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