
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 \( y = x^2 + 4x + 3 \) and \( y = mx + c \) at two points which are exactly \( 7 \) units apart. If the line \( y = mx + c \) passes through the point \( (1,6) \), and \( c \neq 0 \), find the equation of the line. Enter your answer in the form " \( y = mx + c \)".

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