
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 $g(x) \geq f(x)$.
2. Find the minimum value of $y = g(x) - f(x)$ within the range found in part 1.

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