
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
In a gathering of 40 people, there are 25 people who all know each other and 15 people among which 5 know exactly 3 people each from the group that knows each other, and the remaining 10 don't know anyone. People who know each other hug, and those who don't know each other shake hands. Calculate the number of handshakes that occur within the group.

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