
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
Line $m$ has the equation $y = 4x + 2$. Line $n$ has the equation $y = kx + 3$. Lines $m$ and $n$ intersect at the point $(1, 6)$. Additionally, line $p$ is perpendicular to line $m$ and passes through the intersection point of lines $m$ and $n$. What is the value of $k$?

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