
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 $f(x) = \begin{cases} 2^{-x}, & -1 \leqslant x < 1 \\ \ln x, & 1 \leqslant x \leqslant a \end{cases}$
(1) When $a=2$, if $f(x)=1$, then $x=$ _______ ;
(2) If the range of $f(x)$ is $[0,2]$, then the range of $a$ is _______ .

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