
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 function $f(x) = x^2 + 2a\ln(1-x)$ where $a \in \mathbb{R}$, find the following:
(1) For $a=-2$, determine the intervals where $f(x)$ is monotonic and its extreme value.
(2) If $f(x)$ is monotonic on the interval $[-1, 1)$, find the range of the real number $a$.

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