
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
A society consists of 4 schools, each with 5 members, totaling 20 members. Determine how many possible ways there are to organize a conference under the following conditions:
i. The society must choose one of the 4 schools to host the conference.
ii. The host school sends 1 representative to the conference, the nearest neighbor school sends 2 representatives, and the other two schools send 1 representative each.

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