
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 \(a\), \(b\), and \(c\) be distinct real numbers. Simplify the expression \[ \frac{(x - a)^3 + ax}{(a - b)(a - c)} + \frac{(x - b)^3 + bx}{(b - a)(b - c)} + \frac{(x - c)^3 + cx}{(c - a)(c - b)}. \]

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