
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
In a certain region, the price of product A from the beginning of 2015 is expected to be $f(x)=\frac{1}{2}(x^2-12x+69)$ in the $x$-th month, where $x\in\mathbb{N}$ and $x\leqslant 12$. The sales volume of the product in the $x$-th month is $g(x)=x+12$.

1. What is the lowest price of product A in 2015?
2. In which month of 2015 was the sales revenue the lowest, and what was the lowest sales revenue?

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