
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
If the line $2ax-by+14=0$ ($a>0$, $b>0$) and the graph of the function $f(x)=m^{x+1}+1$ ($m>0$, $m\neq 1$) always pass through the same fixed point, and this point always lies inside or on the circle $(x-a+1)^2+(y+b-2)^2=25$, determine the range of values for $\frac{b}{a}$.

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