
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 the function $f(x)=a^{2x}-2a^{x+1}+2 (a > 0, a \neq 1)$ with the domain $x \in [-1, +\infty)$.
1. If $a=2$, find the minimum value of $y=f(x)$.
2. When $0 < a < 1$, if there exists at least one $x_{0} \in [-2, -1]$ such that $f(x_{0}) \leqslant 3$, find the range of $a$.

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