
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
For all positive integers  $n > 1$ , let  $f(n)$  denote the largest odd proper divisor of  $n$  (a proper divisor of  $n$  is a positive divisor of  $n$  except for  $n$  itself). Given that  $N=20^{23}\cdot23^{20}$ , compute
\[\frac{f(N)}{f(f(f(N)))}.\]

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