
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]


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During a New Year's gathering, 6 close friends exchanged gifts. Any two friends could exchange gifts at most once, with each exchange involving the two friends giving a gift to each other. It is known that there were a total of 13 exchanges among these 6 friends. Determine the number of students who received 4 gifts.

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