
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 $f(x)=(x-a)e^{x}$ where $a \in \mathbb{R}$.

(1) When $a=2$, find the equation of the tangent line to the function $f(x)$ at $x=0$.
(2) Find the minimum value of $f(x)$ on the interval $[1,2]$.

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