
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 function $f(x)= \frac {1}{4}x^{4}- \frac {1}{2}ax^{2}$, where $a \in \mathbb{R}$.
(1) When $a=1$, find the equation of the tangent line to the curve $f(x)$ at the point $(2, f(2))$.
(2) Let $g(x) = (x^2 - 2x + 2 - a)e^x - ef(x)$, where $e = 2.71828...$ is the base of the natural logarithm. Discuss the monotonicity of $g(x)$ and determine whether it has any extreme values. If it does, find the extreme values.

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