
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 a function $y = g(x)$, it is known that if the function is shifted 15 units to the right, the resulting graph is the same as the original, i.e., $g(x-15) = g(x)$. What is the smallest positive $b$ such that if the graph of $y = g\left(\frac{x}{3}\right)$ is shifted $b$ units to the right, then we know that the resulting graph is identical to the original graph of $y = g\left(\frac{x}{3}\right)$?

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