
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
The  $n^{th}$  derivative of a function  $f(x)$  (if it exists) is denoted by  $f^{(n)}(x) $ . Let  $f(x)=\frac{e^x}{x}$ . 
Suppose  $f$  is differentiable infinitely many times in  $(0,\infty) $ . Then find  $\lim_{n \to \infty}\frac{f^{(2n)}1}{(2n)!}$ 

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