
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
Suppose $g(x) = f(\frac{x}{4})$ where $f(x)$ is a function with the property that $f(x) = f(x-24)$ for all $x$. Determine the smallest positive $b$ such that if the graph of $y=g(x)$ is shifted $b$ units to the right, then the resulting graph is identical to the original graph of $y=g(x)$.

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