
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 the function $f(x)=ax+b$, where $x \in [a-4,a]$, the graph of the function is symmetric about the origin. Find the range of the function $g(x)=bx+ \frac{a}{x}$, where $x \in [-4,-1]$.

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