
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 man walked a certain distance at a constant pace. If he increased his speed by $\frac{1}{3}$ mile per hour, he would have completed the journey in five-sixths of the time; if he decreased his speed by $\frac{1}{3}$ mile per hour, he would have taken $3\frac{1}{2}$ hours longer. Determine the distance in miles he walked.

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