
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
Three people, A, B, and C, participate in a job interview at a company. Those who pass the interview can sign a formal contract. A says that he will sign the contract as long as he passes the interview. B and C agree that if both of them pass the interview, they will sign the contract together; otherwise, neither of them will sign. It is given that the probability of A passing the interview is $\frac{1}{4}$, and the probability of both B and C passing the interview is $\frac{1}{3}$ each, and the outcomes of the interviews of the three people are independent. Find:<br/>$(Ⅰ)$ The probability that exactly one person passes the interview;<br/>$(Ⅱ)$ The probability that at most one person signs the contract.

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