
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 certain archer has a probability of $\frac{2}{3}$ of hitting the target with each shot, and the results of each shot are independent.<br/>$(1)$ Suppose this archer takes $5$ shots, find the probability of hitting the target exactly $2$ times;<br/>$(2)$ Suppose this archer takes $5$ shots, find the probability of hitting the target $3$ times in a row and missing the target $2$ times.

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