
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 function $y = \log_a(x + 2) - 1$ ($a > 0$, $a \neq 1$), determine the minimum value of $\frac{1}{m} + \frac{2}{n}$ if point A lies on the line $mx + ny + 1 = 0$, where $m > 0$, $n > 0$.

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