
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 some rule, where the new color depends only on the color of the biting and the bitten chameleon. It is known that \$ 2023 \$ red chameleons can agree on a sequence of bites such that they all become blue. What is the smallest \$ \mathrm{k} \$ that guarantees that \$ \mathrm{k} \$ red chameleons can agree on a sequence of bites to become blue?

For example, the rules could be: if a red chameleon bites a green one, the bitten changes color to blue; if a green bites a red, the bitten remains red; if a red chameleon bites a red one, the bitten changes to yellow, and so on. (The specific color change rules may vary.)

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