
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 a quadratic equation in $x$, $x^2-2(1-m)x+m^2=0$, with roots $x_1$ and $x_2$.

(1) Find the range of values for $m$;  
(2) If $x_1^2+12m+x_2^2=10$, find the value of $m$.

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