
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 possible values of  $a\in \mathbb{R}$  and  $n\in \mathbb{N^*}$  such that  $f(x)=(x-1)^n+(x-2)^{2n+1}+(1-x^2)^{2n+1}+a$  

is divisible by  $\phi (x)=x^2-x+1$ 

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