
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 that $f(x) = x^3 + ax^2 - (2a+3)x + a^2$ where $a \in \mathbb{R}$.
(1) If the tangent line of the curve $y = f(x)$ at $x = -1$ is parallel to the line $2x - y - 1 = 0$, find the value of $a$.
(2) If $a = -2$, find the intervals where $f(x)$ is increasing or decreasing and the extreme values.

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