
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 the inverse proportion function $y=\frac{{6-3k}}{x}(k \gt 1$ and $k\neq 2)$ intersects with the linear function $y=-7x+b$ at two points, and the product of the x-coordinates of the two intersection points $x_{1}\cdot x_{2} \gt 0$, please write down a value of $k$ that satisfies the condition.

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