
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
**6.** Let  $H_{n}(x)$  be the *n*th Hermite polynomial. Find $ \lim_{n \to \infty } (\frac{y}{2n})^{n} H_{n}(\frac{n}{y})$ For an arbitrary real y. **(S.5)** $H_n(x)=(-1)^n e^{x^2}\frac{d^n}{dx^n}\left(e^{{-x^2}}\right)$ 

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