
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 toy store purchases a certain toy at a price of 49 yuan per piece for sale, and expects that when the selling price is 50 yuan per piece, 50 toys can be sold per day. Within a certain range, when the selling price of each toy is increased by an average of 0.5 yuan, 3 fewer toys will be sold per day.  
(1) If the selling price of the toy does not exceed 60 yuan per piece, and the total cost of toys sold per day does not exceed 686 yuan, predict the range of the selling price per toy;  
(2) In actual sales, based on the lowest selling price and corresponding sales volume of the toy in (1), the toy store further adjusted the sales plan, increasing the selling price of each toy by $a\%$, thereby reducing the daily sales volume by $2a\%$. When the daily sales profit is 147 yuan, find the value of $a$.

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