
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 equation of the circle $(x+2)^{2}+(y+1)^{2}=1$ has its center at point $A$. If point $A$ lies on the line $mx+2ny+1=0$, where $mn > 0$, then the minimum value of $\dfrac{1}{m}+\dfrac{1}{n}$ is ______.

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