
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 positive real numbers and $a\neq 1$), its graph passes through points $A(1,27)$ and $B(-1,3)$.
(1) Find the values of $a$ and $b$.
(2) If the inequality $a^{x}+b^{x}\geqslant m$ holds true for $x\in[1,+\infty)$, find the range of values for the real number $m$.

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