
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
There are inﬁnitely many ordered pairs  $(m,n)$  of positive integers for which the sum
\[ m + ( m + 1)  +  (   m   +   2)   +... + (   n   - 1 )+n\]
is equal to the product   $mn$ .  The four pairs with the smallest values of   $m$  are  $(1, 1), (3, 6), (15, 35),$  and  $(85, 204)$ . Find three more  $(m, n)$  pairs.

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