
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 certain unit has two vehicles participating in a certain type of accident insurance, where for each vehicle involved in this type of accident within the year, the unit can receive compensation (each vehicle can only receive compensation once). Suppose the probabilities of these two vehicles being involved in this type of accident within a year are $\dfrac{1}{20}$ and $\dfrac{1}{21}$, respectively, and whether each vehicle is involved in an accident is independent of the other. Then, the probability that the unit will receive compensation from this insurance within a year is _______ (express the result as a simplified fraction).

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