
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 certain information transmission process, each piece of information can only be a permutation of a $6$-digit number composed of $0$ or $1$ (digits can be repeated and the first digit can be $0$). Find the probability that a randomly selected piece of information consists of exactly $2$ zeros and $4$ ones.

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