
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 a culturing of bacteria, there are two species of them: red and blue bacteria.

When two red bacteria meet, they transform into one blue bacterium.
When two blue bacteria meet, they transform into four red bacteria.
When a red and a blue bacteria meet, they transform into three red bacteria.

Find, in function of the amount of blue bacteria and the red bacteria initially in the culturing, 
all possible amounts of bacteria, and for every possible amount, the possible amounts of red and blue bacteria.

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