Let
$$
\alpha=\sum_{k=1}^{\infty} \sin ^{2 k}\left(\frac{\pi}{6}\right)
$$
Let $g_a[0,1] \rightarrow \mathbb{R}$ be the function defined by
$$
g(\mathrm{x})=2^{\alpha \mathrm{x}}+2^{\alpha(1-\mathrm{x})}
$$
Then, which of the following statements is/are TRUE?
Select ALL correct options:
A
The minimum value of $g(x)$ is $2^{\frac{7}{6}}$
B
The maximum value of $g(x)$ is $1+2^{\frac{1}{3}}$
C
The function $g(\mathrm{x})$ attains its maximum at more than one point
D
The function $g(\mathrm{x})$ attains its minimum at more than one point
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