
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
In the binomial $(ax^{m}+bx^{n})^{12}$ (where $a > 0, b > 0, m \neq 0, n \neq 0)$, there is a condition that $2m+n=0$. If the term with the largest coefficient in its expansion is the constant term,   

$(1)$ Determine which term it is;   
$(2)$ Find the range for $\frac{a}{b}$.

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