
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
An abstract animal lives in groups of two and three.

In a forest, there is one group of two and one group of three. Each day, a new animal arrives in the forest and randomly chooses one of the inhabitants. If the chosen animal belongs to a group of three, that group splits into two groups of two; if the chosen animal belongs to a group of two, they form a group of three. What is the probability that the $n$-th arriving animal will join a group of two?

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