
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
What is the necessary and sufficient condition for the fraction

$$
\frac{a_{1} x^{2}+b_{1} x+c_{1}}{a_{2} x^{2}+b_{2} x+c_{2}}
$$

to be constant for all values of $x$?

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