
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 commodity was originally priced at $p$ yuan per unit, and $n$ units were sold each month. If the price is increased by $x$ tenths (where $x$ tenths means $\frac{x}{10}$, with $0 < x \leq 10$), the monthly sales volume will decrease by $y$ tenths, and the total sales amount becomes $z$ times the original. (1) Let $y = a x$, where $a$ is a constant satisfying $\frac{1}{3} \leq a < 1$. Express the value of $x$ in terms of $a$ when the sales amount is maximized; (2) If $y = \frac{2}{3} x$, find the range of $x$ values that make the total sales amount greater than the original.

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