
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
Determine the value of $k$ for which the vertical line $x=k$ intersects both the graph of $y=x^2+6x-4$ and the line $y=mx+b$ at two points that are exactly $9$ units apart. The line passes through the point $(2,1)$ with $b\neq 0$. Write the equation of the line in the form "$y=mx+b$".

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