
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
Let $f(\alpha) = \sin^{x}\alpha + \cos^{x}\alpha$, where $x \in \{n | n = 2k, k \in \mathbb{N}_{+}\}$. Using trigonometric transformations, estimate the values of $f(\alpha)$ at $x = 2$, $4$, $6$, and speculate on the range of values of $f(\alpha)$ for general values of $x$ to be ____.

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