
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
In a certain mall, there are two boxes of candies, A and B, priced differently. Box A contains $m$ kg of candies at a price of $a$ yuan/kg, and Box B contains $n$ kg of candies at a price of $b$ yuan/kg. The mall decides to sell the candies from both boxes mixed at a combined price of $\frac{am+bn}{m+n}$ yuan/kg (the mixed price is the total price divided by the total weight).  
(1) If $a=30$, $m=30$, $b=25$, and $n=20$, then the price per kilogram of the mixed candies is _______ yuan/kg.  
(2) If $a=30$ and the mall currently has 100 kg of mixed candies at a unit price of 24 yuan/kg, how much of Candy A must be added to increase the mixed price by 15%?  
(3) If $m=40$ and $n=60$, an equal weight of candies is taken from both boxes A and B; the candies from box A are mixed with the remaining candies from box B, and vice versa. If both mixtures have the same unit price, how much candy is taken from each box?

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