
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
Let \( g(x) = f(\frac{2x}{5}) \) and \( f(x) \) has the property such that \( f(x+10) = f(x) \) for all \( x \). Determine the smallest positive \( b \) such that the graph of \( y = g(x-b) \) is identical to the graph of \( y = g(x) \).

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