
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 $f(x)$ is an increasing linear function on $\mathbb{R}$ and $g(x) = f(x)(x + m)$, with $f[f(x)] = 16x + 5$.
1. Find $f(x)$.
2. When $x \in [1, 3]$, $g(x)$ has a maximum value of 13. Find the value of the real number $m$.

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