
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
Define $f(x)$ to be the minimum value of the three numbers $3x + 1,$ $-\frac{4}{3}x + 3,$ and $\frac{1}{3} x + 9$ for each value of $x.$ Find the maximum value of $f(x).$

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