
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 live red, green, and blue dragons. Each dragon has three heads, each of which always tells the truth or always lies. Moreover, each dragon has at least one head that tells the truth. One day, 530 dragons sat around a round table, and each one said:

- 1st head: "The dragon to my left is green."
- 2nd head: "The dragon to my right is blue."
- 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}
user