
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 4 red pegs, 3 blue pegs, and 2 green pegs to be placed on a triangular peg board formed by 3 rows increasing from 1 to 3 pegs from top to bottom. In how many ways can the pegs be placed so that no (horizontal) row or (vertical) column contains two or more pegs of the same color? (Similar pegs are indistinguishable from each other.)

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