
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
Bag A and B contain several uniform red and white balls. The probability of drawing a red ball from bag A is $\frac{1}{3}$, and the probability of drawing a red ball from bag B is $p$.
(1) Drawing with replacement from bag A, each time drawing one ball, a total of 5 times  
① The probability of exactly drawing 3 red balls; ② The probability of drawing a red ball on the first, third, and fifth draws.  
(2) If the ratio of the number of balls in bags A and B is 1:2, and after combining the balls from A and B, the probability of drawing a red ball is $\frac{2}{5}$, find the value of $p$.

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