
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 the function $f(x) = x^{\alpha} + 1$ (where $\alpha \in \mathbb{Q}$) have a domain of $[-b,-a] \cup [a,b]$, with $0 < a < b$. If the function $f(x)$ has a maximum value of 6 and a minimum value of 3 on the interval $[a,b]$, then the sum of the maximum and minimum values of $f(x)$ on the interval $[-b,-a]$ is ____.

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