
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 a certain job fair in $2016$, there were $5$ job seekers with similar qualifications, denoted as $A,B,C,D,E$. They applied for secretary positions, but there were only $2$ such positions available, so only $2$ out of the $5$ people were hired. If all $5$ people had an equal chance of being hired, calculate the probability of the following events:

$(1)$ $C$ gets one of the positions;

$(2)$ $B$ or $E$ gets one of the positions.

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