
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 $$y_{1} = 4^{0.2}, y_{2} = \left( \frac{1}{2} \right)^{-0.3}, y_{3} = \log_{\frac{1}{2}}8$$, determine the relationship between $y_1$, $y_2$, and $y_3$ in terms of their magnitude.

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