
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 \( f(x) = x^4 + ax^3 + bx^2 + cx + d \), where \( a \), \( b \), \( c \), and \( d \) are constants, if \( f(1) = 1 \), \( f(2) = 2 \), and \( f(3) = 3 \), find the value of \( f(0) + f(4) \).

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