
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
$J$ takes $45$ minutes less time than $L$ to travel a distance of $45$ miles. $J$ travels $\frac {1}{2}$ mile per hour faster than $L$. If $y$ is $J$'s rate of speed in miles per hours, then $J$'s time for the distance is:
A) $\dfrac{y + \frac {1}{2}}{45}$  
B) $\dfrac{y - \frac {1}{2}}{45}$  
C) $\frac{45}{y+\frac{1}{2}}$  
D) $\frac{45}{y}$

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