
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 the equation in terms of $x$, $kx^2+(2k-1)x+k-1=0$ (1), has only integer roots, and the quadratic equation in terms of $y$, $(k-1)y^2-3y+m=0$ (2), has two real roots $y_1$ and $y_2$  
(1) When $k$ is an integer, determine the value of $k$;  
(2) Under the condition of (1), if $m>-2$, express $y_1^2+y_2^2$ in terms of an algebraic expression of $m$.

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