
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
If the conic $\Gamma_{1}: F_{1}(x, y) = 0$ and the conic $\Gamma_{2}: F_{2}(x, y) = 0$ have four common points, then the equation of any conic passing through these four points can be expressed as
$$
\lambda F_{1}(x, y) + \mu F_{2}(x, y) = 0 \quad (\lambda, \mu \in \mathbf{R}).
$$

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