
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 that \( x_{1} = 1, x_{2} = 2, x_{3} = 3 \) are three zeros of \( f(x) = x^{4} + ax^{3} + bx^{2} + cx + d \), find \( f(0) + f(4) \).

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