
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 that $$α ∈ \{-2, -1, -\frac{1}{2}, \frac{1}{3}, \frac{1}{2}, 1, 2, 3\}$$, determine the values of α which make the power function $f(x) = x^{α}$ an even function that is also decreasing on the interval $(0, +∞)$.

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