
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 holds a promotional lottery event where each customer draws a ball from a lottery box containing four identical balls labeled with 0, 1, 2, and 3. The customer draws one ball, records its number, then returns it to the box before drawing a second time (drawing twice consecutively). If the sum of the two drawn balls equals 6, the customer wins the first prize; if the sum equals 5, the customer wins the second prize; and if the sum equals either 4 or 3, the customer wins the third prize. The probability of a customer winning the third prize is __________.

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