
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 $f(x) = \begin{cases} \frac {a}{x-1}, & x\leq0 \\ \lg x, & x>0 \end{cases}$, where $a\neq0$. If $f(x)=0$, then $x= \boxed{\text{\_\_\_\_\_\_}}$; if the equation $f(f(x))=0$ has a unique solution, then the range of values for the real number $a$ is $\boxed{\text{\_\_\_\_\_\_}}$.

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