
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 basketball player scores $1$ point if the shot is made and $0$ points if it is missed. It is known that player A has a shooting percentage of $P$.  
$(1)$ If the score of shooting $1$ time is denoted as $\xi$, find the maximum value of the variance $D\xi$;  
$(2)$ When the maximum value of $D\xi$ is obtained in $(1)$, find the probability that player A scores $4$ points in $5$ shots.

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