
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 marked with 0, two cards marked with 1, and three cards marked with 2. Bag $B$ contains 7 cards: four cards marked with 0, one card marked with 1, and two cards marked 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 cards drawn are 0.
(2) The probability that the product of the numbers on the three cards drawn is 4.

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