
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 $y=\log_{a}(x+3)-1 (a > 0, a\neq 1)$, whose graph always passes through point $A$. If point $A$ is on the line $mx+ny+1=0$ where $mn > 0$, find the minimum value of $m^{2}+ \frac{1}{4}n$.

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