
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 the function

$$
f(x)=\frac{(x+a)^{2}}{(a-b)(a-c)}+\frac{(x+b)^{2}}{(b-a)(b-c)}+\frac{(x+c)^{2}}{(c-a)(c-b)}
$$

where \(a\), \(b\), and \(c\) are distinct real numbers. Determine the range of the function.

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