
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
Find all integers  $k$  such that all roots of the following polynomial are also integers:   $$ f(x)=x^3-(k-3)x^2-11x+(4k-8). $$  

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