
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
There are chameleons of five different colors living on an island. 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 biter 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 minimum $k$ such that $k$ red chameleons can certainly agree to become blue?

For example, the rules could be as follows: if a red chameleon bites a green one, the bitten chameleon changes its color to blue; if a green chameleon bites a red one, the bitten chameleon remains red (i.e., "changes color to red"); if a red chameleon bites a red one, the bitten chameleon changes its color to yellow, and so on. (Specific rules for color change may be different.)

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