
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
The integers \(a\) and \(b\) are coprime (i.e., their greatest common divisor is 1), with \(a > b\). Compare the numbers:

\[ 
m = \left\lfloor\frac{a}{b}\right\rfloor + \left\lfloor\frac{2a}{b}\right\rfloor + \cdots + \left\lfloor\frac{(b-1)a}{b}\right\rfloor 
\]

and

\[ 
n = \left\lfloor\frac{b}{a}\right\rfloor + \left\lfloor\frac{2b}{a}\right\rfloor + \cdots + \left\lfloor\frac{(a-1)b}{a}\right\rfloor 
\]

where \(\lfloor x \rfloor\) denotes the floor function of the real number \(x\).

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