
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 $y = nx + c$ at two points which are exactly $4$ units apart. If the line $y = nx + c$ passes through the point $(2,5)$, and $c \neq 0$, find the equation of the line. Enter your answer in the form "$y = nx + c$".

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