
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 $y=\log_a(x+3)-1$ (where $a>0$ and $a\neq1$) always passes through a fixed point A. If point A lies on the line $mx+ny+1=0$, with $m>0$ and $n>0$, the minimum value of $\frac{1}{m}+\frac{1}{n}$ is ( ).

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