
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 $a$, $b$ are positive real numbers and $a \neq 1$), the graph passes through point A$(1, 27)$ and B$(-1, 3)$:
(1) Find the values of $a$ and $b$.
(2) If the inequality $a^x + b^x \geq m$ always holds for $x \in [1, +\infty)$, find the range of the real number $m$.

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