
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
Suppose there are 6 red pegs, 5 green pegs, 4 blue pegs, 3 yellow pegs, and 2 orange pegs to be placed on a square peg board, such that no (horizontal) row or (vertical) column contains two or more pegs of the same color. (Any two pegs of the same color are indistinguishable.) How many ways can these pegs be distributed so that the condition is satisfied?

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