
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 6 yellow pegs, 5 red pegs, 4 green pegs, 3 blue pegs, 2 orange pegs, and 1 black peg to be placed on a larger triangular peg board. In how many ways can the pegs be arranged such that no (horizontal) row or (vertical) column contains two or more pegs of the same color? All pegs of the same color are indistinguishable.

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