
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
If $(m^n)^2 = p^r = t$ and $p^s = (m^u)^3 = q$, find the relationship between $n, r, s, u$.
**A)** $2ur = 3ns$  
**B)** $ur = ns$  
**C)** $3ur = 2ns$  
**D)** $ur + ns = 2rs$  
**E)** $3un = 2sr$

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