
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 male and 1 female teachers, and School B having 1 male and 2 female teachers. If one teacher is randomly selected from each school, what is the probability that the two selected teachers are of the same gender?

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