
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 real numbers \(x\), \(y\) satisfying \(x > y > 0\), and \(x+y \leqslant 2\), find the minimum value of \(\dfrac{2}{x+3y}+\dfrac{1}{x-y}\).

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