
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
Simplify and then evaluate the expression: $$\frac{{{x}^{2}}-4xy+4{{y}^{2}}}{{{x}^{2}}-xy}\div (x+y-\frac{3{{y}^{2}}}{x-y})+\frac{1}{x}$$, where $(x, y)$ is the solution to the system of equations $$\begin{cases} x-y=5 \\ x+2y=2 \end{cases}$$.

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