
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
A woman cycled a particular distance at a steady rate. If her speed had increased by $\textstyle\frac{1}{3}$ miles per hour, she would have completed the journey in three-quarters of the time. If her speed had reduced by $\textstyle\frac{1}{3}$ mile per hour, she would have taken $1\textstyle\frac{1}{2}$ hours more. Find the distance she cycled and the original speed.
A) 2 miles and 0.75 mph
B) 2.5 miles and 0.85 mph
C) 3 miles and 1 mph
D) 3.5 miles and 1.15 mph

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