
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
A function  $f$ , defined for the set of integers, is such that  $f(x)=x-10$  if  $x>100$  and  $f(x)=f(f(x+11))$  if  $x \leq 100$ .

Determine, justifying your answer, the set of all possible values for  $f$ .

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