
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 person walks a certain distance at a constant speed. If he walks $\frac{1}{2}$ mile per hour faster, he would take $\frac{4}{5}$ of the original time to walk this distance. If he walks $\frac{1}{2}$ mile per hour slower, he would take $2 \frac{1}{2}$ hours more to walk this distance. Find the distance he walked.

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