
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
There are 7 academic competition winners, among whom the Chinese winners are $A\_1$, $A\_2$, the Mathematics winners are $B\_1$, $B\_2$, the English winners are $C\_1$, $C\_2$, and the Physics winner is $D\_1$. A representative team of 3 is to be selected from the competition winners, with at most one winner from each subject.

1. Calculate the probability that $B\_1$ is selected;
2. Calculate the probability that the representative team contains a Physics winner.

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