
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 the expression and find its numerical value for the given values of the variables:

1) \( x^{2}-\frac{x^{3}-4 x y^{2}}{x(x-2 y)+y^{2}} \cdot \frac{x^{2}-2 x y+y^{2}}{x-2 y} \), where \( x=-\frac{1}{2}, y=-5 \);
2) \( \frac{a^{2}+a b+b^{2}}{a^{3}+2 a^{2} b+a b^{2}}+\frac{b-a}{(a+b)^{2}} \cdot \frac{a}{a-b}-\frac{a}{a^{2}+a b} \), where \( a=-1 \frac{1}{3}, b=-\frac{3}{4} \);
3) \( \left(\frac{m n}{m^{2}-n^{2}}+\frac{n}{2 n-2 m}\right) \frac{m^{2}-n^{2}} {2 n} \), where \( m=6 \frac{1}{2}, n=-1.5 \);
4) \( \frac{5 m+5 n}{m-n}\left(\frac{m}{m+n}-\frac{m}{m^{2}-n^{2}}\right) \), where \( m=3 \frac{1}{2}, n=-\frac{1}{2} \).

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