
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 the function $f(x)=\begin{cases}2^{x}-a, & x < 1 \\ 4(x-a)(x-2a), & x\geqslant 1\end{cases}$,

(1) If $a=1$, then the minimum value of $f(x)$ is;

(2) If $f(x)$ has exactly $2$ zeros, then the range of the real number $a$ is.

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