
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
Rewrite the polynomial $f(x)=1-x+x^{2}-x^{3}+\cdots-x^{19}+x^{20}$ in terms of the polynomial $g(y)=a_{0}+a_{1} y+\cdots+a_{20} y^{20}$, where $y=x-4$. Find the value of $a_{0}+a_{1}+\cdots+a_{20}$.

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