
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 club has $5$ members from each of $4$ different schools, totaling $20$ members. Determine the number of possible ways to arrange a presidency meeting under the following conditions:
i. The club must choose one of the $4$ schools at which to host the meeting, and
ii. The host school sends $3$ representatives to the meeting, and each of the other three schools sends $2$ representatives.

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