
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 shopping mall lottery event, there are four balls numbered 0, 1, 2, and 3 in a lottery box. Each time a ball is drawn and then put back, two draws are made consecutively. Winning the first prize if the sum of the two drawn ball numbers equals 5, winning the second prize if the sum equals 4, and winning the third prize if the sum equals 3.

(1) Calculate the probability of winning the third prize.
(2) Calculate the probability of winning a prize.

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