
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 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 coefficient of the largest term in the expansion is only for the $6$th and $7$th terms, find the value of $m$.

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