
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 \( x, y \in \mathbb{R} \), the set \( A=\left\{(x, y) \mid x^{2}-3xy+4y^{2}=\frac{7}{2}\right\} \) and \( B=\{(x, y) \mid kx+y=2\} (k>0) \), find the value of \( k \) when the intersection of \( A \) and \( B \) has exactly one element.

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