
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 \( x^{4} + a_{1} x^{3} + a_{2} x^{2} + a_{3} x + a_{4} = (x+2)^{4} + b_{1}(x+2)^{3} + b_{2}(x+2)^{2} + b_{3}(x+2) + b_{4} \). Define the mapping \( f: (a_{1}, a_{2}, a_{3}, a_{4}) \rightarrow (b_{1}, b_{2}, b_{3}, b_{4}) \), then \( f[(10, 30, 38, 21)] = \) ?

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