
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 line $ax-2by=2$ ($a > 0,b > 0$) passes through the center of the circle $x^{2}+y^{2}-4x+2y+1=0$, the minimum value of $\dfrac {4}{a+2}+ \dfrac {1}{b+1}$ is \_\_\_\_\_\_.

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