
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
In an office, there are 5 teachers with only 3 computers available for use. The teachers using the computers do so independently of one another.
(1) If in a certain period of the morning, the probabilities of teachers A, B, and C needing to use a computer are $\frac{1}{4}$, $\frac{2}{3}$, and $\frac{2}{5}$ respectively, find the probability that exactly two of these teachers will need to use a computer during that period.
(2) If in a certain period of the afternoon the probability that each teacher needs to use a computer is $\frac{1}{3}$, calculate the average number of computers that will be in use during this period and the probability that the demand for computers cannot be met.

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