
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
 $n$  balls are placed independently uniformly at random into  $n$  boxes. One box is selected at random, and is found to contain  $b$  balls. Let  $e_n$  be the expected value of  $b^4$ . Find   $$ \lim_{n \to 
\infty}e_n. $$  

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