
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 quadratic equation about $x$: $x^{2}+2mx+2m+1=0$.
(I) If the equation has two roots, one of which is in the interval $(-1,0)$, and the other is in the interval $(1,2)$, find the range of $m$.
(II) If both roots of the equation are in the interval $(0,1)$, find the range of $m$.

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