
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 $\left\{\begin{array}{l}2x+y=4\\ x+2y=5\end{array}\right.$, complete the following calculations:<br/>$(1)$ Find the values of $x-y$ and $x+y$;<br/>$(2)$ Find the value of $(\frac{1}{3}x^2-\frac{1}{3}y^2)(x^2-2xy+y^2)$.

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