
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 $f(x) = b \cdot a^x$ (where $a$ and $b$ are constants, $a > 0$, $a \neq 1$) and its graph passes through points A(1, $\frac{1}{6}$) and B(3, $\frac{1}{24}$).

(1) Find $f(x)$.

(2) If the inequality $\left(\frac{1}{a}\right)^x + \left(\frac{1}{b}\right)^x - m \geq 0$ always holds for $x \in [1, +\infty)$, find the range of values for $m$.

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