
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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A senior high school student wishes to apply for the independent admission exams of 3 out of 6 universities. However, since the exam times of two of these universities coincide, the student cannot apply to both of these universities at the same time. Calculate the number of different ways the student can apply. (Answer with a number)

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