
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
Define \(L(x) = x - \frac{x^3}{3}\) for every real number \(x\). For a positive integer \(n\), define \(b_n\) by
\[
  b_n = L \Bigl( L \Bigl( \cdots L \Bigl( \frac{25}{n} \Bigr) \cdots \Bigr) \Bigr),
\]
where there are \(n\) iterations of \(L\). Determine the value \(n b_n\) approaches as \(n\) approaches infinity.

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