
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
Given the equation $x^{4}+a_{1}x^{3}+a_{2}x^{2}+a_{3}x+a_{4}=(x+1)^{4}+b_{1}(x+1)^{3}+b_{2}(x+1)^{2}+b_{3}(x+1)+b_{4}$, define the mapping $f(a_{1},a_{2},a_{3},a_{4})=b_{1}-b_{2}+b_{3}-b_{4}$. Find the value of $f(2,0,1,6)$.

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