
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 \\(S_{k}=1^{k}+2^{k}+3^{k}+\ldots+n^{k}\\), for \\(k=1\\), \\(2\\), \\(3\\), \\(\ldots\\), observe the following equations:

\\({{S}_{1}}=\dfrac{1}{2}{{n}^{2}}+\dfrac{1}{2}n\\),

\\({{S}_{2}}=\dfrac{1}{3}{{n}^{3}}+\dfrac{1}{2}{{n}^{2}}+\dfrac{1}{6}n\\),

\\({{S}_{3}}=\dfrac{1}{4}{{n}^{4}}+\dfrac{1}{2}{{n}^{3}}+\dfrac{1}{4}{{n}^{2}}\\),

\\({{S}_{4}}=\dfrac{1}{5}{{n}^{5}}+\dfrac{1}{2}{{n}^{4}}+\dfrac{1}{2}{{n}^{3}}-\dfrac{1}{30}n\\),

\\({{S}_{5}}=A{{n}^{6}}+\dfrac{1}{2}{{n}^{5}}+\dfrac{5}{12}{{n}^{4}}+B{{n}^{2}}\\),

\\(\ldots\\)

From this, we can infer that \\(A-B=\)_______.

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