
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 shopping mall is holding a promotional lucky draw event where each customer draws a ball from a box containing balls numbered 0, 1, 2, and 3. A ball is drawn twice, each time recording the number and then returning the ball to the box. A first prize is awarded if the sum of the two drawn numbers is equal to 6, a second prize if the sum is equal to 5, and a third prize for sums of 4 or 3.
(1) What is the probability of winning the third prize?
(2) What is the probability of winning any prize?

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