
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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There are 4 problems in a mathematics competition. The scores are allocated as follows: 2 marks for a correct answer, -1 mark for a wrong answer, and 0 marks for a blank answer. To ensure that 3 candidates will have the same scores, how many candidates, denoted as $S$, must there be at least in the competition? Find the value of $S$.

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