
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
You have a triangular peg board and need to place 6 yellow pegs, 5 red pegs, 4 green pegs, 3 blue pegs, and 2 orange pegs. How can you place the pegs so 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.)

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