
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
In a store promotion event, suppose the probability of winning the first prize is 0.1, the probability of winning the second prize is 0.2, and the probability of winning the third prize is 0.4. Calculate in this lottery:
(1) What is the probability of winning a prize?
(2) What is the probability of not winning any prize?

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