
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

In an underwater kingdom, there are octopuses with seven and eight legs. Those with 7 legs always lie, and those with 8 legs always tell the truth. One day, three octopuses had the following conversation:

Green Octopus: "Together, we have 21 legs." Blue Octopus (to Green): "You are lying!" Red Octopus: "Both of you are lying!"

1) Could the Green Octopus have told the truth? Why?
2) How many legs did each octopus have? (Justify your answer.)

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