
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 constants and $a > 0,a\neq 1$, its graph passes through points $A(1,6)$ and $B(3,24)$.

(I) Find the analytical expression of function $f(x)$;

(II) If the inequality ${(\dfrac{1}{a})^{x}}+{(\dfrac{1}{b})^{x}}-m\geqslant 0$ holds true for $x\in(-∞,1]$, find the range of values for the real number $m$.

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