
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 the land of Draconia, there are red, green, and blue dragons. Each dragon has three heads, and each head always tells the truth or always lies. Additionally, each dragon has at least one head that tells the truth. One day, 530 dragons sat around a round table, and each of them said:

- 1st head: "To my left is a green dragon."
- 2nd head: "To my right is a blue dragon."
- 3rd head: "There is no red dragon next to me."

What is the maximum number of red dragons that could have been at the table?

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