
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 \(d,\ e,\) and \(f\) be distinct real numbers. Simplify the expression
\[
\frac{(x + d)^4}{(d - e)(d - f)} + \frac{(x + e)^4}{(e - d)(e - f)} + \frac{(x + f)^4}{(f - d)(f - e)}.
\]

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