
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 polynomial  $f(x)=1-x+x^2-x^3+\cdots-x^{19}+x^{20}$  is written into the form  $g(y)=a_0+a_1y+a_2y^2+\cdots+a_{20}y^{20}$ , where  $y=x-4$ , then  $a_0+a_1+\cdots+a_{20}=$ ________.

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