
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 sum of the binomial coefficients of the expansion of $(x+ \frac{m}{x})^n$ is 256,  
(1) find $n$;  
(2) if the constant term in the expansion is $\frac{35}{8}$, find the value of $m$;  
(3) if the expansion has only the 6th and 7th terms as the terms with the maximum coefficients, find the value of $m$.

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