
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 Grade 8 Class 4 of our school, there are 57 students. If every two students shake hands with each other once, then each student needs to shake hands     times, and the whole class needs to shake hands     times in total.

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