
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
People who know each other hug, and people who do not know each other shake hands at a conference with $5$ people who are completely new and know no one, $10$ people who know no one from other groups but know everyone within their own group, and $25$ people who all know each other. Calculate the total number of handshakes that occur.

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