
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
Xiao Ming, Xiao Hong, and two other students each applied for independent recruitment exams at two universities, A and B, with exactly two students applying to each university. What is the probability that Xiao Ming and Xiao Hong did not apply to the same university?

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