
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
The function $g$ is defined on the set of integers and satisfies 
\[
g(n)= \begin{cases}  
n-4 & \mbox{if }n\ge 500 \\
g(g(n+5)) & \mbox{if }n<500 
\end{cases}
\]
Find $g(72)$.

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