
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
There is only one value of \(k\) for which the line \(x=k\) intersects the graphs of \(y=x^2+4x+4\) and \(y=mx+b\) at two points which are exactly \(8\) units apart. If the line \(y=mx+b\) passes through the point \((2,9)\), and \(b \neq 0\), find the equation of the line in the form "y=mx+b".

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