
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
1) It is known that the sequence \( u_{1}=\sqrt{2}, u_{2}=\sqrt{2+\sqrt{2}}, u_{3}=\sqrt{2+\sqrt{2+\sqrt{2}}}, \ldots, u_{n}=\sqrt{2+u_{n-1}} \) converges. Find its limit.
2) Find the limit of the sequence \( u_{n}=\frac{2^{n}}{n!} \).



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