
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
On an island, there are chameleons of five colors. When one chameleon bites another, the color of the bitten chameleon changes according to a certain rule, and the new color depends only on the color of the biting chameleon and the color of the bitten chameleon. It is known that 2023 red chameleons can agree on a sequence of bites, after which all of them will become blue. What is the smallest $k$ such that $k$ red chameleons can guarantee to agree on a sequence of bites so that they all become blue?

For example, the rules could be such: if a red chameleon bites a green one, the bitten chameleon changes color to blue; if a green chameleon bites a red one, the bitten chameleon remains red, that is, "changes color to red"; if a red chameleon bites a red one, the bitten chameleon changes color to yellow, and so on. (Specific rules for color changes may be different.)

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