
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 school plans to form a basketball team and needs to select reserve players from each class. It is stipulated that players who achieve a first-level shooting score can be considered as candidates. During the selection process, each player can shoot up to 5 times, and it is also stipulated that once a player is confirmed to be selected, they do not need to shoot anymore. If a player scores 2 shots, they are considered second-level, and scoring 3 shots qualifies them as first-level. According to past technical statistics, a student named Wang Ming has a probability of $$\frac {2}{3}$$ of scoring each shot, and the outcomes of each shot are independent of each other.  
(1) Calculate the probability that Wang Ming is determined to be second-level after shooting 3 times;  
(2) Given that Wang Ming has already been selected, calculate the probability that he actually needed 5 shots to be selected under this condition.

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