
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 $25$ units to the right, then the resulting graph is identical to the original graph of $y=g(x)$.

What is the smallest positive $a$ such that if the graph of $y=g\left(\frac{x}{4}\right)$ is shifted $a$ units to the right, the resulting graph is identical to the original graph of $y=g\left(\frac{x}{4}\right)$?

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