
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 expansion of $\left(mx-1\right)^{n}$ has the sum of the coefficients equal to the sum of the binomial coefficients and the binomial coefficient of the 6th term is the largest, calculate the number of different sets of ordered real number pairs (m, n).

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