
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 three sets of cards in red, yellow, and blue, with five cards in each set, labeled with the letters $A, B, C, D,$ and $E$. If 5 cards are drawn from these 15 cards, with the condition that all letters must be different and all three colors must be included, how many different ways are there to draw the cards?

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