
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
Find the number of ordered pairs of integers $(m,n)$ such that $mn \geq 0$ and

\[m^3 + n^3 + 117mn = 36^3.\]
A) 36
B) 37
C) 38
D) 39
E) 40

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