
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 the binomial expansion of $(ax+\frac{b}{x})^n$ ($a>0$, $b>0$), let $A$ be the sum of all binomial coefficients, $B$ be the sum of all item coefficients, and $C$ be the constant term value. If $A=B=256$, $C=70$, determine the term containing $x^6$.

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