
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
Distribute 5 students to Peking University, Shanghai Jiao Tong University, and Tsinghua University for direct admission, with each university admitting at least one student. How many different distribution methods are there?

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