
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
Given that a high school senior is preparing to take the college entrance exams for independent admissions, with 6 colleges to choose from, but with the restriction that he cannot apply to two specific colleges at the same time, determine the number of different ways this student can choose the colleges to apply to.

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