
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 vectors $\overset{→}{a} =(x,2)$ and $\overset{→}{b} =(1,y)$, where $x > 0$ and $y > 0$. If $\overset{→}{a} \cdot \overset{→}{b} =1$, find the minimum value of $\dfrac{1}{x} + \dfrac{2}{y}$.

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