
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 $a\in \mathbb{R}$. If there exists a function $f(x)$ with domain $\mathbb{R}$ that satisfies the following two conditions:<br/>
$(1)$ For any $x_{0}\in \mathbb{R}$, the value of $f(x_{0})$ is either $x_{0}$ or $x_{0}^{2}$;<br/>
$(2)$ The equation $f(x)=a$ has no real solutions,<br/>
then the range of values for $a$ is ____.

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