
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 two lines $y=k_{1}x+3k_{1}+b$ and $y=k_{2}x+3k_{2}+b$, where $k_{1}\cdot k_{2} \lt 0$, find the value of $|k_{1}-k_{2}|$ if the area of the triangle formed by these two lines and the $y$-axis is $9$.

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