
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 $f(x)$ be defined as
$$f(x)= \begin{cases} -x^{2}+ax, & x\leq 1\\ ax-1, & x > 1 \end{cases}$$
If there exist $x_1, x_2 \in \mathbb{R}, x_1 \neq x_2$, such that $f(x_1) = f(x_2)$ holds, then the range of the real number $a$ is _________.

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