
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
A, B, and C participate in a job interview at a company. Those who pass the interview can sign the contract officially. A states that he will sign the contract as long as he passes the interview, while B and C have agreed that they will both sign the contract if both pass the interview; otherwise, neither will sign. Assume that the probability of each person passing the interview is $\frac{1}{2}$, and whether one passes the interview or not does not affect the others. Find:  
(I) The probability that at least one person passes the interview;  
(II) The probability that no one signs the contract.

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