
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 functions $f(x)=\log_{2}(x+1)$ and $g(x)=\log_{2}(3x+1)$,

1. Find the range of $x$ that satisfies $g(x)\geqslant f(x)$.
2. Determine the range of the function $y=g(x)-f(x)$ when $x\in[0,+\infty)$.

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