
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 competition, there are eight contestants consisting of five females and three males. If three contestants are chosen randomly to progress to the next round, what is the probability that all selected contestants are female? Additionally, from those who do not proceed, one is selected as a host. What is the probability that this host is male?

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