
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 that $f(x) = a^x - b$ (where $a > 0$, $a \neq 1$, and $b \in \mathbb{R}$), and $g(x) = x + 1$. If for every real number $x$, we have $f(x) \cdot g(x) \leq 0$, then the minimum value of $\frac{1}{a} + \frac{4}{b}$ is ______.

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