
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
Liam, Mia, and Noah play a game where each starts with $2$. A bell rings every 12 seconds. Each time it rings, each of the players who currently have money independently and at random chooses one of the other two players to give $1. What is the probability that, after the bell rings $2020$ times, each player will have exactly $2$?
A) $\frac{1}{9}$
B) $\frac{1}{4}$
C) $\frac{1}{3}$
D) $\frac{1}{2}$
E) $\frac{2}{9}$

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