
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 five cards in a bag, three of which are red, numbered $1, 2, 3$, and two are blue, numbered $1, 2$.
(1) Calculate the probability that the two cards drawn from these five cards have different colors and the sum of their numbers is less than $4$.
(2) Now, add a green card numbered $0$ to the bag. From these six cards, calculate the probability that the two cards drawn have different colors and the sum of their numbers is not greater than $4$.

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