
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 an exam with \( n \) questions, a student answered 15 out of the first 20 questions correctly. For the remaining questions, he answered \(\frac{1}{3}\) of them correctly. All questions have the same scoring weight. If the student's total score is 50%, determine the number of different values that \( n \) can take.

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