
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
A student is preparing to take the college entrance exams for independent admissions and needs to choose 3 out of 6 colleges to apply to. However, since the exam times for two of the colleges coincide, the student cannot apply to both of these colleges at the same time. Determine the number of different application methods for this student.

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