
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 Journalism Department at the University of Fairyland Commonwealth has 5 spots: 2 for the daytime program and 3 for the evening program. Four chickens (three black and one white) are applying for these spots. A spot for each chicken is reserved immediately after it submits its application, and the order of applications is completely random. When both the daytime and evening spots are available, each chicken chooses either one with equal probability. Find the probability that at least one black chicken will be admitted to the daytime program.

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