
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
The Faculty of Journalism at the University of the Fairytale Commonwealth has 5 target spots: 2 for the daytime program and 3 for the evening program. Four hens are applying for these spots: three black ones and one white one. Each hen's spot is reserved immediately after it submits its application, and the order of submission is strictly random. If there are vacancies in both programs, each hen chooses either program with equal probability. Find the probability that at least one black hen enrolls in the daytime program.

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