
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 in the expansion of $(1+m\sqrt{x})^{n}$ (where $m$ is a positive real number) is $256$, and the coefficient of the term containing $x$ in the expansion is $112$.  
$(1)$ Find the values of $m$ and $n$;  
$(2)$ Find the sum of the binomial coefficients of the odd terms in the expansion;  
$(3)$ Find the coefficient of the $x^{2}$ term in the expansion of $(1+m\sqrt{x})^{n}(1-x)$.

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