
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 $f$ is defined on the set of integers and satisfies 
\[f(n)= 
\begin{cases}  
n-4 & \mbox{if } n\ge 1200 \\  
f(f(n+6)) & \mbox{if } n<1200 
\end{cases}\]
Find $f(125)$.

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