
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 a linear function $f(x)=ax+b$ is an increasing function on $\mathbb{R}$, and $f(f(x))=16x+5$.

(Ⅰ) Find the values of $a$ and $b$;

(Ⅱ) Let $g(x)=(x+m)\cdot f(x)$, if $g(x)$ is monotonically increasing on $[1,+\infty)$, find the range of the real number $m$.

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