
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 fixed point always falls within or on the circle $(x - a + 1)^2 + (y + b - 2)^2 = 25$, then the range of $\frac{b}{a}$ is ___.

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