
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 that $a_2 \neq 0$ and $r$ and $s$ are the roots of $a_0 + a_1x + a_2x^2 = 0$, determine for which values of $x$ the equality $a_0 + a_1x + a_2x^2 = a_0\left(1 - \frac{x}{r}\right)\left(1 - \frac{x}{s}\right)$ holds.

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