
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 conference of $40$ people, there are $25$ people who all know each other and $15$ people who know no one. People who know each other wave, and people who do not know each other shake hands. How many handshakes occur between people who do not know each other?

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