
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
Employees from department X are 30, while the employees from department Y are 20. Since employees from the same department do not interact, the number of employees from department X that will shake hands with the employees from department Y equals 30, and the number of employees from department Y that will shake hands with the employees from department X also equals 20. Find the total number of handshakes that occur between employees of different departments.

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