
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
School A and School B each have 3 teachers signing up for a teaching support program, with School A having 2 males and 1 female, and School B having 1 male and 2 females.  
(Ⅰ) If one teacher is randomly selected from each of the schools, what is the probability that the two selected teachers are of the same gender?  
(Ⅱ) If 2 teachers are randomly selected from the total of 6 teachers, what is the probability that the two selected teachers come from the same school?

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