
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 certain store sells a craft item, with an average daily sales of 20 pieces and a profit of $40 per piece. In order to reduce inventory quickly, the store decides to take appropriate price reduction measures. After investigation, it was found that within a certain range, for every $1 decrease in the unit price of each craft item, the store can sell an additional 2 pieces on average per day.  
$(1)$ If the store wants to make a profit of $1050 per day by selling this craft item, how much should the price of each craft item be reduced by?  
$(2)$ Can the store make a daily profit of $1600 by reducing the price? Please explain the reason.

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