
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 bag contains five cards, three of which are red and numbered $1$, $2$, $3$ respectively, and two are blue and numbered $1$, $2$ respectively.
(I) Calculate the probability of drawing two cards from the above five cards such that their colors are different and the sum of their numbers is less than $4$.
(II) Now, a green card numbered $0$ is added to the bag. Calculate the probability of drawing two cards from these six cards such that their colors are different and the sum of their numbers is less than $4$.

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