
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
At a gathering of 35 people, there are 25 people who all know each other, 5 people who know no one, and 5 people who each know exactly 18 people from the first group. People who know each other hug, and people who do not know each other shake hands. Calculate the total number of handshakes that occur.

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