
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 $x^2-2x+m+1=0$.
(1) If the equation has two real roots, find the range of $m$;
(2) If the two real roots of the equation are $x_1$, $x_2$, and $x_1+3x_2=2m+8$, find the value of $m$.

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