
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
The Mathematics Department of Nankai University holds a Mathematics Festival called "$\pi$ Day" every year on March 14th. They plan to purchase two types of Rubik's cubes, $A$ and $B$. The price of each $A$ type Rubik's cube is $15$ yuan, and the price of each $B$ type Rubik's cube is $22$ yuan. If the Mathematics Department plans to purchase a total of $40$ Rubik's cubes of these two types, with the quantity of $B$ type Rubik's cubes not less than the quantity of $A$ type Rubik's cubes, and the school can provide a maximum of $776$ yuan in funding, then the minimum number of $A$ type Rubik's cubes to be purchased is ______.

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