
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
For each value of \(x\), \(g(x)\) is defined to be the minimum value of the three numbers \(3x + 3\), \(\frac{1}{3} x + 2\), and \(-\frac{2}{3} x + 8\). Find the maximum value of \(g(x)\).

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