
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
Consider a function \( y = f(x) \) such that shifting its graph 30 units to the right results in the identical graph \( y = f(x) \). Determine the smallest positive \( b \) such that shifting the graph of \( y = f\left(\frac{x}{3}\right) \) \( b \) units to the right will result in a graph identical to the original graph of \( y = f\left(\frac{x}{3}\right) \).

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