
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
In the set of real numbers $\mathbb{R}$, a new operation "$\ast$" is defined. For any $a, b \in \mathbb{R}$, $a \ast b$ is a uniquely determined real number, and it has the properties:  
$(1)$ For any $a \in \mathbb{R}$, $a \ast 0 = a$;  
$(2)$ For any $a, b \in \mathbb{R}$, $a \ast b = ab + (a \ast 0) + (b \ast 0)$.  
Then, the minimum value of the function $f(x) = (e^{x}) \ast \frac{1}{e^{x}}$ is $\boxed{\text{B: }3}$.

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