
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
If  $f$  is a polynomial, and  $f(-2)=3$ ,  $f(-1)=-3=f(1)$ ,  $f(2)=6$ , and  $f(3)=5$ , then what is the minimum possible degree of  $f$ ?

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