
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 in terms of $x$: $x^2 + 2mx + 2m + 1 = 0$.

(1) Determine the nature of the roots when $m = 1$.

(2) 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 values for $m$.

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