
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 $x^4+a_1x^3+a_2x^2+a_3x+a_4 = (x+1)^4+b_1(x+1)^3+b_2(x+1)^2+b_3(x+1)+b_4$, define the mapping $f: (a_1, a_2, a_3, a_4) \rightarrow (b_1, b_2, b_3, b_4)$. Determine the image of the point $(4, 3, 2, 1)$ under this mapping.

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