
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
There are two bags, $A$ and $B$. Bag $A$ contains 6 cards: one card with 0, two cards with 1, and three cards with 2. Bag $B$ contains 7 cards: four cards with 0, one card with 1, and two cards with 2. One card is drawn from bag $A$ and two cards are drawn from bag $B$, making a total of three cards. Find:
(1) The probability that all three drawn cards are 0.
(2) The probability that the product of the numbers on the three drawn cards is 4.

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