
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
Let $a,$ $b,$ $c,$ and $d$ be distinct real numbers. Simplify the expression
\[
\frac{(x + a)^4}{(a - b)(a - c)(a - d)} + \frac{(x + b)^4}{(b - a)(b - c)(b - d)} + \frac{(x + c)^4}{(c - a)(c - b)(c - d)} + \frac{(x + d)^4}{(d - a)(d - b)(d - c)}.
\]

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