
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 that the linear function $f(x)$ is an increasing function on $\mathbb{R}$, and $g(x)=f(x)(x+m)$, with $f(f(x))=16x+5$:
1. Find the expression for $f(x)$.
2. If $g(x)$ is monotonically increasing on the interval $(1, +\infty)$, find the range of the real number $m$.

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