
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 shooter is undergoing shooting training. Assuming the probability of hitting the target with each shot is $\dfrac{3}{5}$, and the results of each shot are independent of each other. It is known that the shooter fired $5$ times, calculate:  
$(1)$ The probability of hitting the target only on the first, third, and fifth shots;  
$(2)$ The probability of hitting the target exactly $3$ times.

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