
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
How many solutions does the system of equations have in general?

$$
\begin{gathered}
a x^{2} + b x y + c y^{2} = d \\
a_{1} x^{2} + b_{1} x y + c_{1} y^{2} = d_{1}
\end{gathered}
$$

In particular, how many solutions does the system in question 280 have?

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