
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 company purchases a batch of machines for production. According to market analysis, the total profit $y$ (in ten thousand yuan) obtained from the products produced by each machine is related to the machine's operating time $x$ (in years) as $y = -x^2 + 18x - 25$ ($x \in \mathbb{N}^*$). Then, when each machine operates for \_\_\_\_\_ years, the annual average profit is maximized, and the maximum value is \_\_\_\_\_ ten thousand yuan.

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