
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 a first-degree function and $g(x)$ is a second-degree function, and $f[g(x)]=g[f(x)]$.
1. Find the analytical expression of $f(x)$;
2. If $y=g(x)$ is tangent to the $x$-axis and $y=f(x)$, and $g(0)= \frac {1}{16}$, find the analytical expression of $g(x)$.

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