
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 the function $f(x)=x^{2}+ax+4$, if there exists $x_{0} \in \mathbb{R}$ such that $f(x_{0})=x_{0}$, then $x_{0}$ is called a fixed point of $f(x)$. It is known that $f(x)$ always has two different fixed points when $x \in [1,3]$. The range of the real number $a$ is \_\_\_\_\_\_.

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