
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
Mr. Wang drives from his home to location $A$. On the way there, he drives the first $\frac{1}{2}$ of the distance at a speed of 50 km/h and increases his speed by $20\%$ for the remaining distance. On the way back, he drives the first $\frac{1}{3}$ of the distance at a speed of 50 km/h and increases his speed by $32\%$ for the remaining distance. The return trip takes 31 minutes less than the trip to $A$. What is the distance in kilometers between Mr. Wang's home and location $A$?

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