
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 travels from location A to location B, covering a total distance of $500m$. Along the way, they must cross a river with a width of $xm$. Unfortunately, they dropped an item somewhere along the path. If the item is dropped in the river, it cannot be found, but if it's not dropped in the river, it can be retrieved. Given that the probability of finding the item is $\frac{4}{5}$, determine the width of the river.

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