
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 $f(x)$ defined on the set of real numbers $R$, 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 $f(x)$. It is known that the function $f(x) = x^2 + 2ax + 1$ has no fixed points. Determine the range of values for $a$.

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