
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
Consider the line \( y = \dfrac{1}{2}x + 3 \) and another line \( L \) that runs parallel to the given line and is \( 5 \) units away from it. The correct equation for line \( L \) could be:
A) \( y = \dfrac{1}{2}x + 3 + \dfrac{5\sqrt{5}}{2} \)
B) \( y = \dfrac{1}{2}x + 3 - \dfrac{5\sqrt{5}}{2} \)
C) \( y = \dfrac{1}{2}x + 5 \)
D) \( y = \dfrac{1}{2}x \)
E) \( y = \dfrac{1}{2}x - 2 \)

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