
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
There are three types of stocks. The sum of the number of shares of the first two types equals the number of shares of the third type. The total value of the second type of stock is four times the value of the first type of stock. The total value of the first and second types of stocks equals the total value of the third type of stock. The price per share of the second type of stock is 1.6 to 2 yuan more expensive than the first type of stock, and the price per share of the third type of stock is not less than 4.2 yuan and not more than 6 yuan. Find the maximum and minimum percentage of the total number of shares that the first type of stock accounts for.

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