
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
An expert group conducted an assessment of the information technology application capabilities of young teachers in a certain school. The assessment plan is to randomly select 3 young teachers under the age of 45 for evaluation. If 2 or more (including 2) teachers pass the evaluation, the school will pass the information technology application capability assessment. It is known that there are 10 young teachers under the age of 45 in the school, including 1 information technology expert. The probability of the information technology expert passing the evaluation is $\frac{3}{4}$, and the probability of other teachers passing the evaluation is $\frac{1}{2}$.
$(1)$ Find the probability that exactly two teachers pass the evaluation;
$(2)$ Given that the school passed the information technology application capability assessment, find the probability of the information technology expert being selected.

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