
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
$K$ takes $30$ minutes less time than $M$ to travel a distance of $45$ miles. $K$ travels \(\frac {1}{2}\) mile per hour faster than $M$. If \(x\) is $K$'s rate of speed in miles per hours, then $K$'s time for the distance is:
**A)** \(\frac{45}{x + \frac{1}{2}}\)
**B)** \(\frac{x - \frac{1}{2}}{45}\)
**C)** \(\frac{45}{x}\)
**D)** \(\frac{x}{45}\)
**E)** \(\frac{45x}{x - \frac{1}{2}}\)

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