
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
Given \\(x\\), \\(y \in \mathbb{R}^{+}\\), and satisfying \\(\frac{1}{x} + \frac{2}{y} = 2\\), the range of values for \\(8x + y\\) is \_\_\_\_\_\_.

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