
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 math exam has 4 fill-in-the-blank questions, worth a total of 20 points. Each question is worth 5 points if answered correctly, and 0 points otherwise. The first question is designed so that all students can answer it correctly. The probability of answering the remaining three questions correctly is P, $$\frac {1}{2}$$, and $$\frac {1}{4}$$ respectively, and the correctness of each question is independent of the others.
(1) When $$P= \frac {2}{3}$$, find the probability that a student will get a perfect score on the fill-in-the-blank questions.
(2) If the probability of a student scoring 10 points on the fill-in-the-blank questions is equal to the probability of scoring 15 points, find the value of P.

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