
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
Circle $C_{1}(x-m)^{2}+(y-2n)^{2}=m^{2}+4n^{2}+10$ $(mn > 0)$ and circle $C_{2}:(x+1)^{2}+(y+1)^{2}=2$ intersect such that $C_{1}$ bisects the circumference of $C_{2}$; find the minimum value of $\dfrac {1}{m}+ \dfrac {2}{n}$.

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