
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
Throw  $ n$  balls in to  $ 2n$  boxes.　Suppose each ball comes into each box with equal probability of entering in any boxes.
Let  $ p_n$  be the probability such that any box has ball less than or equal to one. Find the limit  $ \lim_{n\to\infty} \frac{\ln p_n}{n}$ 

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