
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 a function $f(x)=\left\{\begin{array}{l}{-{x}^{2}+ax, x\leq 1}\\{2ax-5, x>1}\end{array}\right.$, if there exist $x_{1}$, $x_{2}\in \mathbb{R}$ and $x_{1}\neq x_{2}$ such that $f(x_{1})=f(x_{2})$, then the range of real number $a$ is ____.

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