
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
For a function $f(x)$ defined on the domain of real numbers, if there exists a real number $x_0$ such that $f(x_0) = x_0$, then $x_0$ is called a fixed point of the function $f(x)$. If the function $f(x) = x^2 + ax + 1$ has no fixed points, then the range of the real number $a$ is $\boxed{(-1,3)}$.

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