
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 $y=a^x$ $(a > 0, a \neq 1)$ in the interval $[1, 2]$, the sum of its maximum and minimum values is $6$. If the function $f(x) = a^x + \log_a x + b$ has a zero point in the interval $(1, 2)$, find the range of the real number $b$.

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