
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 that $x$ and $y$ are positive numbers satisfying $x > y$ and $x + 2y = 3$. Find the minimum value of $$\frac{1}{x-y} + \frac{9}{x+5y}.$$
A) $\frac{8}{3}$
B) $\frac{11}{4}$
C) $4$
D) $2$

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