
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
After a market survey, it is identified that when the price of a certain commodity per ton is $x$ thousand yuan ($1 < x < 14$), the monthly supply of the commodity is $y_1$ tons, with $y_{1}=ax+\frac{7}{2}a^{2}-a$ ($a > 0$); the monthly demand for the commodity is $y_2$ tons, with $y_{2}=-\frac{1}{224}x^{2}-\frac{1}{112}x+1$. The quantity sold in a month is equal to the supply when the demand is greater than the supply; otherwise, the quantity sold is equal to the demand. The monthly sales revenue is the product of the selling quantity and the selling price.

(1) Given that $a=\frac{1}{7}$, if the commodity's price for a certain month is $x=7$, calculate the sales revenue for that month (rounded to the nearest Yuan).

(2) The price when the demand equals the supply is referred to as the equilibrium price. If the equilibrium price for the commodity is not lower than 6 thousand yuan per ton, determine the range of values for the real number $a$.

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