
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
During extracurricular activities, several basketball enthusiasts are practicing spot shooting under the guidance of a physical education teacher. It is agreed that each person can shoot up to $10$ times. If a student makes a consecutive shot for the first time on the $n$th shot, the student will score $12-n$ points and stop shooting. For example, if a student makes two consecutive shots, they will score $10$ points and stop shooting. It is known that student A has a shooting probability of $\frac{2}{3}$ for each shot. The probability that student A will stop shooting after exactly the $2$nd shot, scoring $5$ points, is ______.

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