
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 the graph of a function, \( y = g(x) \), has the property that if it is shifted \( 30 \) units to the left, then the resulting graph is identical to the original graph of \( y = g(x) \). What is the smallest positive \( b \) such that if the graph of \( y = g(2x) \) is shifted \( b \) units to the left, then the resulting graph is identical to the original graph of \( y = g(2x) \)?

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