
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 \( A \). If point \( A \) lies on the line \( \frac{x}{m} + \frac{y}{n} + 1 = 0 \), and \( m, n > 0 \), then the minimum value of \( 3m + n \) is _____.

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