
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
Determine the number of ordered pairs of integers $(p,q)$ such that $pq \ge 0$ and 
\[ p^3 + q^3 + 110pq = 35^3. \]
A) 34
B) 35
C) 36
D) 37
E) 38

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