
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 radius  $r$  of a circle with center at the origin is an odd integer. 
There is a point ( $p^m, q^n$ ) on the circle, with  $p,q$  prime numbers and  $m,n$  positive integers. 
Determine  $r$ .

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