
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 $6$ units apart. If the line $y=mx+b$ passes through the point $(2,3)$, find the equation of the line. Enter your answer in the form "$y = mx + b$".

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