
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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Given four students participated in a mathematics competition, with each student choosing between Problem A and Problem B, where solving Problem A correctly earns 30 points and incorrectly results in a 30 point loss, while solving Problem B correctly earns 10 points and incorrectly results in a 10 point loss. If the total score of the four students is zero, determine the number of different scoring situations.

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