
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 \( M(x) = x - \frac{x^3}{3} \) for every real number \( x \). If \( n \) is a positive integer, define \( b_n \) by
\[
  b_n = M \Bigl( M \Bigl( M \Bigl( \cdots M \Bigl( \frac{20}{n} \Bigr) \cdots \Bigr) \Bigr) \Bigr),
\]
where there are \( n \) iterations of \( M \). For example,
\[
  b_4 = M \Bigl( M \Bigl( M \Bigl( M \Bigl( \frac{20}{4} \Bigr) \Bigr) \Bigr) \Bigr).
\]
As \( n \) approaches infinity, what value does \( n b_n \) approach?

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