
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 employer conducts a recruitment process comprising two stages: a written test and an interview. The written test includes two questions, A and B. The probability of a candidate answering questions A and B correctly are $\frac {1}{2}$ and $\frac {1}{3}$, respectively. The candidate must answer both questions correctly to proceed to the interview stage. During the interview, the candidate must answer two questions, C and D, each with a probability of $\frac {1}{2}$ of being answered correctly. The candidate will be hired if they answer at least one interview question correctly (each question is independent in terms of answering correctly or incorrectly).

(I) Calculate the probability of the candidate being hired.
(II) Let $\xi$ represent the number of questions the candidate answers correctly. Calculate $P(\xi=1)+P(\xi=3)$.

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