
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
Given that a positive integer $n$ can be decomposed as $n=p\times q$ ($p$ and $q$ are positive integers, and $p\leqslant q$), determine the value of $S(128)$, where $S(n)=\frac{p}{q}$ is the ratio of the factors $p$ and $q$ in the best decomposition of $n$.

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